Might as well. I've been considering doing this for a while, actually, because it's a subject that comes up often and it'd be handy to have this to refer people to. From the top of my head (will probably update this later):
This will be pretty lengthy, and detailed, because it's something I intend to refer to later, and keep working on, so bear with me.
Updated on March 17th 2017.
The game world
Impassable terrain
HOI3: there were provinces you simply couldn't enter because their infrastructure level was below two.
HOI4: now you can enter any province, but some will have such a high attrition rate they are in practice not feasible to traverse.
Rivers
HOI3: the game only models rivers and straits.
HOI4: the game now has two kinds of rivers. Rivers can freeze during winter.
Diplomacy and politics
Coups, civil wars, and intervention
HOI3: civil wars are handled by historical events and decisions. You can stage coups in foreign countries. Intervention in civil wars is handled by events that do nothing but increase relations, or by lend-leasing abstracted "IC".
HOI4: now civil wars are a dynamic feature, which can theoretically break out anywhere. Intervention can take the form of actual supplies, planes, and other equipment that is physically sent to the recipient, which can make a significant difference if two minor countries without tanks of their own are fighting, and one of them can suddenly field T-34s.
Peace conferences
HOI3: come victory, winners enforce war goals, and territory is largelly divided by war goals set before the war, and who is occupying which provinces.
HOI4: now there is a peace conference system in which the victors take turns claiming the spoils of war, with various factors such as war score affecting who can claim what.
Factions and declarations of war
HOI3: there are only three factions, and if you join one, you're stuck in it permanently. Anyone can declare war provided their neutrality is sufficiently low and threat is sufficiently high.
HOI4: anyone can create factions, and what system of government you have now matters far more, thanks to such things as World Tension. Declarations of war require Casus Belli. You can 'defect from' factions if things are starting to go belly-up.
Declarations of war
HOI3: you could declare war if the target's threat was higher than your neutrality.
HOI4: now there's a system that requires you to justify your war, which in turn is restricted by the world tension system and other factors.
Leadership
HOI3: you assigned ministers, but your research and production body was represented by abstracted "leadership", which was spent on espionage, research, diplomacy and so on.
HOI4: you pick ministers as well as what companies and organisations to put in charge of research and production. Political capital (political power) is accumulated and spent to enforce decisions.
Industry
Factory construction
HOI3: you can build factories anywhere, even on tiny islands and in regions where nobody even lives.
HOI4: now you actually need people to work your factories, so the maximum number of factories you can build in a state is tied to its population density, and some areas, such as the aforementioned tiny islands, can't have industry at all.
Types of industry
HOI3: factories produce resources to generate abstracted "industrial capacity" which can be be used to build anything.
HOI4: now you have three types of industry: civilian, military and naval. Factories have to be assigned to build specifc items such as field hospitals, interceptors, infantry equipment, destroyers, and artillery guns.
Production and equipment
HOI3: abstracted "IC" is spent producing abstracted "reinforcements". Practical builds up over time and affects all units of a given type. For example, factories building level four tank divisions still benefit from practical acquired from building level one, two, and three tank divisions.
HOI4: now the game tracks subs, destroyers, aircraft, tanks, trucks and infantry gear packages individually. Divisions don't just regain "strength", but physically receive tanks, infantry gear, and so on. Practical builds up per unit and per production line, so adding factories or switching from building a level one tank to a level two tank will hurt production efficiency, but switching to a different variant or a similar vehicle will hurt production efficiency less. You can research various kinds of new vechiels, such as self-propelled artillery, based on the chassis of "primary" vehicles.
Supply
HOI3: supply is generated in the capital only, and flows outwards to units according to a system that was not easy to manage, and not properly understood by players.
HOI4: now supply is generated by large cities, and the system is more readily understandable.
Military
Experience
HOI3: you have to wage war for your troops to gain experience.
HOI4: now you can have your forces conduct exercises to gain experience, up to a certain level, during peace-time.
Division makeup
HOI3: your smallest building block is the brigade. You can prioritise divisions for upgrades and reinforcements, or deny them upgrades/reinforcements if you're running short.
HOI4: now the smallest building blocks are companies, and you can assign divisions support assets such as signal battalions or field hospitals. You have three levels of supply priority, not two. Divisions can be assigned custom icons.
Division design
HOI3: you can instantly start producing the optimal production templates.
HOI4: now you have to spend strategic experience, accumulated by exercises and warfare, on building or editing division templates, simulating how changes to division makeup was often in response to actual lessons from the battlefield.
Divisions, navy and air force composition
HOI3: you have one kind of each unit -- one type of small tank, one type of fighter, one type of submarine, for example, and upgrades affect all units of this type. That is, you have "Interceptor wing level 1", which upgrades to "Interceptor wing Level 2". Individual units within divisions are abstracted into division upgrades and "strength". A tank division is for all intents and purposes a single unit, with organisation, strength, and various upgrades.
HOI4: every new upgrade is now a different vehicle; in effect, you can't build 100 level one interceptors and then upgrade them to level two interceptors. Units can be further customised by the variant system. Divisions now track individual pieces of equipment, tanks and whatnot within them, so a tank division, instead of just having 10 000 men and "100% strength", will have "10 000 men (with 1000 sets of infantry equipment), 4 KV-1s, 21 T-34s, 30 T-28s, 20 Self-Propelled 88mm AT guns, 22 Self-Propelled AA guns, 60 trucks, a field hospital, and a signal company". Update 17.3: You can even custom-tailor which divisions get which equipment variant, and have, for example, one division get basic Panzer IVs while another gets an up-armoured version.
Planes, submarines and destroyers
HOI3: aircraft, subs and destroyers are abstracted into "wings" and "flotillas" which are, for all intents and purposes, single units.
HOI4: each aircraft, sub and destroyer is now modelled individually, which allows for sub and destroyer flotillas to saturate naval zones more effectively, and aircraft to fight in a more realistic manner. Now, small groups of individual planes will dogfight, rather than just two "air wings".
AI and Battle Planners
HOI3: the AI was very rudimentary and could only be given very simple instructions. The Battle Planner only allowed you to draw on the map.
HOI4: now the battle planner is used to give instructions to the AI, allowing you to give them fairly complex instructions.
Operational warfare
HOI3: you can tell your troops to begin operations on the fly.
HOI4: now you have to give your men time to prepare for offensives, or they will not fight at full efficiency.
Amphibious invasions
HOI3: you could invade anywhere, whenever you wanted, range permitting, as long as you had at least one transport and one unit that could be carried on board.
HOI4: now you need naval superiority to launch the invasion, and the invasion force needs time to prepare. The invasion ships can be intercepted, unlike in HOI3 where you were guaranted to make it to shore once the invasion had started. Troops will be unable to fire on defenders while on their way to shore, but will still be fired upon.
Nuclear bombing
HOI3: you could drop the bomb wherever you wanted to, range permitting.
HOI4: now you need air superiority over the target region.
...and probably lots more that I can't think of at the moment
.I like to say that if HOI3 came after HOI4, and not the other way around, people would probably still complain as much, or more, that it was dumbed down. The division designer would be gone, you would have generic "industry" instead of three types of factories, you would no longer have vehicles, equipment and guns individually tracked, you would no longer be able to form factions, supplies would only be generated at your capital, and there would be no more variants. Sure, you would also get an OOB system and various other goodies, but the game would still feel dumbed down due to the stuff you were losing.
On balance, I, personally, feel HOI4 is a big step in the right direction, rather than a dumbed-down version of HOI3. I'm looking forward to the added depth more than I miss the features that have been cut.
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