I can also strongly recommend this book to those wanting to understand naval warfare of the era, it is however by no means the most detailed source available because its a book written to be accessible for the keen reader, there are plenty more intricate and fine detailed sources on the topic, especially those written as PhD theses or papers opening up state archives and recordings to those who don't have access to them. The best books on galleys proper I've found are pretty much unanimously written in Italian with some good sources in Spanish, although fewer and further between. Gunpowder and Galleys is still a fantastic opening book and I'd still recommend it to people of all levels of knowledge.
I disagree, there is no better source for galleys in era of gunpowder, which is the period that concerns EU4, than this book. At least not in English. Although I cannot verify for Italian and Spanish, I have my doubts any more thorough work can exists for this particular configuration. Galleys in general perhaps but we are talking about galleys in gunpowder era, which is what concerns us here because we are talking about specific comparisons between round, square-rigged sailships and lateen-rigged galleys.
Galleys under oar really weren't very fast vessels, with a typical cruising speed of around 5kn with most finding a sprint of 7 and in some cases 8kn which could be held by experienced and well exercised and provisioned oarsmen for about 15-20 minutes, at which point the crew would be exhausted. The idea that they are somehow faster than their sailing counterparts is kind of ridiculous
@Titanius Puffin has gone into a very nice basic understanding of sailing from a modern perspective and during the galley based era combative round ships would at least match the sprint speed of the average galley for roughly 220 degrees to the wind, although they might struggle to keep up with the smaller more lightly armed variants.
Galleys under oar, especially because of their lateen-rigging were faster vessels in Mediterranean. Under good wind conditions square-rigged vessels are obviously better under sails but this is a condition that didn't exist commonly or reliably in Mediterranean. That's why lateen-rigged low sailing vessels like polacca and xebecs were used even after galleys became uncommon. It's irrelevant minutae to compare square-rigged vessels under perfect wind conditions to galleys under oars, because it's not important here in the particular context we are dealing with, which is the 16th and 17th century naval warfare involving fleets.
I don't understand why you are trying to sell the Galleass as a defensive style ship, they were used combatively in a very similar way to tanks in ww2 era. they were very much offensive breakthrough ships meant for breaking formations of the enemy for smaller ships to then take advantage of this aggressive disruption of the line with their role most fitting their aggressive shock value. The galleass also has very little to do with large merchant galleys and we much more a modern take on the research and restoration of technical skills used to build and power what is effectively a resurrection of the quinquereme and while some technical skills came from the practical skills needed to build effective large merchant galleys it was much more to do with ancient shipbuilding theory being expanded and experimented on in the era.
These are all irrelevant, because for one, galleasses saw very limited use. We are to look at practical examples here and galleasses were present in few of them. Most important one involving war fleets on both sides is Lepanto and here their slow speed and low manoeuvrability was noted by the captains and they were fittingly used defensively as anchors for the galley formations. All 6 of the galleasses in Lepanto were refitted merchant vessels and all 6 were similarly fitted with high forecastles, their design was clearly meant as defensive platforms to prevent boarding and they were used very much like roundships as opposed to low forecastle Venetian galleys that focused on speed, manoeuvrability with lower firepower.
Looking at perhaps the most famous galley battle in history, Lepanto you can quite clearly see the Christian fleet, especially the Spanish had taken significant numbers of large sailing warships, mostly galleons with the intent on using them as they proved their effective combative ability at battles such as Djerba and Preveza despite for various reasons the Christian combined fleets still losing, denying the intent of use of these large powerful vessels isn't something that really makes sense for some of the most major engagements of the 16th century or the transition to sail warfare over the period and Preveza especially proves the point you made wrong about the Iberians not using their ships in the Mediterranean. Lepanto as an example doesn't really show the vast numbers of fighting sail ships because they didn't take part in the engagement due to wind conditions and the nature of the battle taking place in the geographic area it did but they were still a hugely significant part of the fleet.
This is completely ignoring the facts on the ground and is actually patently false. There were no Spanish galleons present in Lepanto, moreover of all the galleys on Christian side in Lepanto, more than half, including all Galleasses were Venetian, most of rest was Genoese either under a Genoese patrician's ownership or leased to Spain and remainder were a mixed from Napoli and Papal states. Spanish didn't bring any sailing vessels to Lepanto, most importantly even if they wanted they couldn't bring anything but sailing ships because they didn't have a galley fleet. Spanish did use sailing vessels in Tunis at aftermath of Lepanto, exactly as mentioned as support and siege vessels. If only warships available to Spain was square-rigged sailships and if they were to be a boon rather than an obstacle why wouldn't have they brought them to Lepanto, especially when a counter-invasion was expected? Galley war fleets fought in formations, usually with up to 60 ships in a single cluster with a centre and two wings. A square-rigger sailship has no place in this formation because of type of warfare being fought. Holy League side was also much more densely manned by actual soldiers on galleys, the galleys also had their spurs cut before battle meaning that they fully anticipated, expected and planned around boarding.
On the comments made about the polacca and xebec again show some real lack of understanding, the high period of the xebec saw some real monstrously sized vessels of that type sailing the Mediterranean some of which fielding around 50 guns during the early to mid 18th century easily capable of attacking the typical 12 pounder frigates of their contemporary patrol navies and swift enough to avoid larger ships, especially into the wind. The polacca on the other hand was not a low sided ship at all, the entire point of the polacca was that it was built up high for a ship its size purely to deter boarding and make it easy for a merchant crew to fend off much larger pirate/corsair crews.
This is again irrelevant minutiae, while this is correct in 18th century it is irrelevant to comparison between galleys and sailships. First of all Barbary states and general pirates in the area started to switch from light galleys to sailing vessels beginning from 17th century, they were already using low profile sailing vessels with lateen riggings sometimes supported by oars. Polacca are high for galleys but they are low for square-rigged trade vessels that were in line of development that borne from cogs or carracks. This is exactly because galleys could no longer carry enough cannons to to match merchant vessels. Secondly, raids and skirmishes involving a few vessels and outright naval battles between fleets cannot be compared. For one the smaller skirmishes necessarily favour roundships, especially because corsairs intend to board and take over the ship, secondly merchant vessels do not want to engage corsairs proactively or offensively so the disadvantages of roundships in formation or in offensive were irrelevant to them. This is opposite to galley formations which being offensive, able to force engagements or otherwise move with a strategical or tactical military objective. Circumstances, aims, advantages and disadvantages are all different when few corsair ships engage few merchant vessels. A galley war fleet wants to engage and destroy enemy fleets to prevent reinforcements and transfer troops for coastal sieges.
Round ships weren't really more open ended than their oared contrasting navy vessels, the very prevalence of the Lantern galley proves this, huge by design and the centre point of many fleets, again something that contrasted into the ancient world where you'd see much more common use of the hexareme and even octaremes as capital ships. Rounded ships were in no way more open ended, design principles still severely limited the scope of what you could achieve and was very limited by technological progress of the era. The round ship eventually won out in the main theatre of being much more weatherly and being much more easily fitted with heavier and later double hulled systems, this however wasn't really something that helped much in sheltered areas, proving difficult to sail in sheltered coastlines and not really available for much more expansive military duties until there were significant improvements to rigging available.
Roundships were more open-ended in design size, because they weren't limited by geometric constraints of a galley. A galley is a strict balancing act because it's oar powered. If you had read the book I suggested as you claim to have, this is discussed exhaustively there. For a galley to increase in size to accommodate more cannons it also needs more oarsmen, and to accommodate more oarsmen it needs more cargo space, which limits its strategic scope and speed under oars. A galley essentially has a very short limit on how large it can be because linear increase in its size requires exponential increase in oarsmen and oarsmen supplies. Moreover because of positioning of oarsmen and generaly vulnerability of the crew they cannot use broadside cannons. Lanternas weren't necessarily larger, they were important because they were commandships with specific functions. Ancient world galley warfare is irrelevant to us here as cannons doesn't become involved. A galley was limited in design space, because becoming too large limited its strategic and tactical use.
Galleys weren't just made outdated by the reasons you have suggested either, the situational advantages of sailing warships vs oared is one that comes into an interesting question outside of the Mediterranean, you see some interesting examples happening in the Caribbean during the mid to late colonial period again used for the same reason they were maintained within the Mediterranean, even the young USA had a small galley collection at one point, this also extends to the popularity of half galleys and archipelago sloops, with smaller warships of the 17th and 18th century fighting with square rigs but also adopting oars in a hybrid set up to give them greater advantage in coast and island hopping in areas with high rates of raiding or maritime theft.
Taking the example of movement away from Galleys during the Cretan war again this doesn't hold up to evidence, as the Venetian navy did exercise building a number of large sailing warships, even dedicated major sheds in the northwest part of the Venetian arsenal to these ships which had originally been set up to build galleass but became the core of the hybrid fleet. The Cretan war did however see a shift of Venice moving more aligned towards typical European naval thought after the successes of the Giove Fulminante class warship, despite this its still important to stress that Venice like other navies still didn't stop producing galleys in the 18th century, something that would prove incredibly useful to the Venetian fleet in the last 3 wars fought before the dissolution of the republic, the 1st Morean war, 2nd Morean war and the Venetian Tunisian war all of which involved heavy reliance on galleys in the conflicts. You even see this example from the records of ships captured from Venice by France in 1797 with 24 galleys, 17 Xebecs and 13 Felluca falling into french hands, this also doesn't count the numbers stationed at Corfu which fled the port escaping capture which would likely estimate another 8-10 Galleys, 10-12 xebecs, and 5-8 Felluca.
Here again there is the fundamental misunderstanding of naval skirmishes between few merchant ships, merchant vessels or patrols against corsairs or shallows. Galleys retained their fundamental utility as amphibious vessels of shallow draft with exceptional manoeuvrability without dependence on wind conditions, thus they were used for patrols or amphibious operations. Much like how boats with oars are still used by coastguards today, however to say a modern destroy didn't outclass a galley would be insanity. Fundamental change that happened was while in initial stages of maritime gunpowder warfare galleys presented a superior firepower ability because of their agility and independence of wind which put roundships to secondary and supportive roles, due to limited amount of guns available to be outfitted to ships, amphibious nature of warfare and outcome being decided by boarding, galleys became obsolete because they were much more limited in size which they already reached in capacity in 16th century. A galley had to sacrifice a lot in its strategic and tactical mobility to become larger, and even then there was a very short limit because of dependence on increasing amount of oarsmen and their cargo space. This wasn't an issue when the amount of cannons that could be outfitted to ships was limited and thus the multi-purpose utility and manoeuvrability of galleys was more valuable, however as mass cannon production became available the galleys became limited only to their role as amphibious vessels.
Simply put, while both Venice and Ottomans still used galleys as their primary war vessels and sail ships in supportive roles, because of changes in circumstances and realisations during the 2 decades war they both increased the number of their sailships and reduced number of their oared vessels, by the end of the war both Venice and Ottomans became primarily sailship naval powers, with oared vessels entirely reduced to auxiliary roles in their perspective capacity (ability to land with oars, independence from wind and all else).
Another point made about the high number of cannons puts no effort into judging effectiveness of guns, with the Venetian 74 and 76 gun ships Corona and Leon Trionfante being no doubt the most heavily armed warships of the 18th century, despite being launched in 1711 and 1716 respectively. However on a more standardised point of costing, producing, equipping manning and maintaining the large heavy fleets of the late 18th and early 19th century was vastly more costly during say the Napoleonic era than the massive fleet eras of say the height of the Galley in the 16th century or the massive fleet battles of say the Anglo Dutch wars during the 17th century, something that becomes most evident with merchant shipping costs as the European navies with large expensive and expansive fleets of ships of the line and frigates etc being able to transport goods at much lower prices due to the safety ensured by these expensive warships compared to the much cheaper galley centred fleets of say the Italian nations.
This was always a factor, the reason why Venice was able to have so large fleets was because they already had a large merchant fleet and general dependency on ships so they had the necessary infrastructure and personnel, as well as necessity and incentive to maintain large fleets. Of course the balance between cost, speed, seaworthiness and maintenance of ships is always important so you didn't want to make massive floating cities with 1000 cannons but the point is a galley's margin for adjustment is narrower and sacrifices much more because of dependence on oarsmen. This is exactly the point here, a galley has a lot of strategic and tactical cost to make adjustments for firepower and durability while sailships are less limited. Specifically, square-rigged sailships are also less limited than lateen-rigged ones when it comes to size, but as you move from oars to lateen-rigs to square-rigs you also depend more on wind conditions. Wind conditions which are predictable and consistent in oceans but unpredictable and limited in closed seas.
Since this became a rather confused discussion, I will reiterate my initial point. I have said in 15th and 16th centuries square-rigged sailships would be no match for galleys in open warfare between war fleets. Because a galley war fleet would simply be able to present more guns, have more manoeuvrability and no dependence on wind and faster movement under suboptimal wind conditions which was the norm in Mediterranean. Advantage of the galley wasn't that it was cheaper, because it wasn't, but rather it was a multipurpose vessel with superior agility to put fewer number of guns to use. When roundship development and methods of cannon founding developed further the sailing ships outclassed galleys in outright naval warfare because they could become bigger, higher and carry more cannons making them very resistant to warfare methods of very costly galley fleets in more cost effective ways. Simply put galleys became impractical because they couldn't become larger to compete with higher drafts and more cannons of sailships especially ships of the line without becoming completely useless in strategic and tactical capacity. Corsairs and patrols have a more dynamic relation to this, as they were not war fleets but rather had specific dynamics and purposes that were not military in nature but economic. Relatively lower xebecs and polaccas were used by both merchants and corsairs because their lateen-rigged sails offered more versatility with wind conditions and their lower drafts meant they could operate closer to shallows.
This didn't mean galleys became useless, it rather meant that they became left behind in the naval war fleet arms race. They still had their purpose to be used, and they could still operate in smaller skirmishes in particular circumstances. Battles between entire war fleets and skirmishes between corsairs and merchants, duties of naval patrols or amphibious operations need to be considered separately. This is something that won't be represented in EU4 naval battles, as in EU4 this would just be privateering in or guarding a trade node.
Simply, my argument was that galleys should always be superior to "heavies" in closed-seas, until when they become obsolete and by which point they are represented by lateen-rigged low-draft sailships anyway. I actually think that "xebecs" and "archipelago frigates" should not be superior, but only evenly matched if even that to "heavies" in closed-seas. The superiority in closed seas should be galley's up to tech 21 but from there on they should not be. I would support a general reduction of cannon count of last three types of "galleys" to make them matched against heavies rather than superior.
Here, as a closing example, a Maltese galley squadron capturing an Ottoman two-decked sailship:
I also apologise for the wall of text.