I've been playing 3AD almost exclusively since getting the game - but on the other hand I would not consider myself to be a terribly good player (for the most part I can at least *hold* my section of the frontline and give some support to those in my flanks) - so take these notes with some grain of salt.
My general sense of the game is that the maps inherently favor infantry-centric battlegroups. And I need to be specific here - I don't mean that 91 Luftlande or any particular Division is going to be OP because it has theoretically a lot of infantry. Rather, what I mean is that a deck that is built with infantry at its core - with all the other elements (e.g. airplanes, tanks, etc) being designed to support this infantry core - tends to be more successful than say a deck full of Panthers or bombers.
And the reason for this is that tanks and other toys tend to have pretty low staying power because of the terrain; especially when they are attacking. Tanks will tend to get "channeled" into fire traps where a few towed ATGs can pick them off (or infantry can ambush them) while airpower needs to run a gauntlet of unspotted anti-air to deliver their bombs and then survive interceptors that chase after them.
Infantry, by contrast, may lose bodies quickly to enemy fire and get pinned down. However, getting them to retreat often also saves most of the remaining squad - as the infantry can quickly get behind cover so long as you're quick with pressing "R" as soon as they get pinned. This means that an infantry squad can be used multiple times to probe/attack/defend over the course of a single engagement - which is great value for a 10-20 point unit compared to having a 100+ point tank blown up by an ATG or Panzerfaust.
When decks are run without the infantry core in mind - such as a 12th SS player who deploys lots of Panthers and few Panzergrenadiers - they very quickly run into trouble. I've already encountered several of them putting their Panthers in open fields where their flank was resting on a hedegrow occupied by my infantry (left unmolested because they weren't calling in more infantry themselves) - which allowed me to bring up 76mm guns to the "flanking" hedgegrow and cause havoc for the tanks. Similarly, there are Luftlande players who seemingly forget their infantry entirely after Phase A and go all-air, which allows my own infantry to start taking back ground with just a few support units even against vaunted Fallshirmjaegers dug-in towns.
Hence, in the specific case of 3AD, the core of the battlegroup should not be its tanks but rather its armored infantry. While I'm still not consistently winning I've had a lot more success once I started paying more attention to my infantry (and their halftracks, which is half of the cost!) and how to support them.
The thing is, I'm somewhat increasingly tempted to run fewer and fewer tanks in the deck - which is contrary to the popular history conception of an "armored division" (which I would argue it itself a historically flawed argument - most Armored Divisions were in fact mostly mechanized Divisions by 1944 - but I digress). Instead I tend to pick stuff that would be better at supporting infantry for very specific tasks.
For instance, I tend to buy artillery early and keep them well supplied - because I find that a single mortar tends to kill a lot of fixed ATGs and AA guns; while the M7 is very good at wrecking infantry pushes or even suppressing tanks. In one particularly memorable battle, where ten German players fought three Allies (we had seven quitters on my team -_-), a single Armored Infantry squad and an M7 basically stopped like twenty Ersatztruppen before they started calling in an endless wave of air power on the position. For heavy AT work I tend to deploy the 76mm guns (especially the two star one) and don't terribly miss having no Shermans or M10s. Even when I'm assaulting a town I tend to prefer the Sherman 105 rather than the regular Sherman; and even when given the choice between a Sherman and an M5 Stuart I tend to go with the latter because of the point savings.
(And yes, I do of course deploy lots of anti-air and aircraft. Because Goddamit Luftlande players stop sending in wave after wave of aircraft!)
In short, while I feel that the 3AD deck is effective, and I feel that the eventual force mix isn't too far off from real history, it feels "off" for people who subscribe to pop-history documentaries and expect Sherman spam.
Now, I can't really say *how* to fix this, but my first instinct would be that it would require a radical change in pricing methodology and playstyle per Division. For instance I feel that 3rd Armored should have greatly reduced prices for the Shermans - even if this leads to the heresy of the Sherman having similar stats compared to the Panzer IV yet is much cheaper (or have its Shermans cheaper compared to other Allied units). The basic idea behind this change is that - unlike most other Divisions - 3AD is one that has tanks which are cheap enough to be risked constantly; whereas infantry is a more limited resource that will tend to be parceled out to support the tanks instead of the other way around.
That said, as I noted - much of the character of the game revolves around the terrain - so making Shermans so cheap you'd buy them over infantry may not be the solution. But I think it's this sort of pretty radical balance mindset that's required to get 3AD where people "expect" it to be as an "Armored" Division; and quite frankly I foresee even more balance whining under that kind of model where you'll have players going "3AD gets 50 point Shermans but Scots pay 150 for their Shermans. 3AD OP!".