A lot of good points have already been made, so I won’t reiterate those but rather add something I haven’t seen anybody mention yet: transparency. The inner workings of ATG are far more transparent than those of TOAW(3 at least, haven’t played 4 yet, but I assume they’re similar in this regard). Now, whether you consider this a good thing or not, or whether it even matters to you, is something else. Some people complain about complex computer wargames that are totally impentrable: they want their games to be like boardgames, in the sense that you can understand most or all of the rules, because if you don’t understand how the game works, you can’t really appreciate the import of the decisions you’re making; in fact, you’re almost not making decisios, according to this argument. Many computer wargames are like this, and for the most part I don’t have a problem with it. But ATG stands out as a shining example of a game where everything is theoretically open to player knowledge. True, I don’t typically look at the detailed combat report to understand exactly how combat works, but the point is that I could. Moreover, I can read the detailed stats of the units and, armed with a decent idea of how combat works, I can get a more detailed sense of what’s going to happen and why.
TOAW has much less detailed stats but much more complicated combat resolution equations (apparently). I’m fine developing an instinct for the combat system and playing by feel - that’s usually what ends up with ATG anyway, and it’s theoretically more “realistic.” Other areas, however, are a bit too opaque for my tastes. For example, in TOAW3 at least, when you watch the review of the enemy’s turn, it gives you no indication of the number of units lost on each side (maybe they changed that in TOAW4, someone else can jump in here) - you just see retreats, unit evaporations, and successful defenses. That’s a bit too opaque for my tastes. And because you can’t see behind the scenes or the nitty gritty details of the units, it’s sometimes hard to get excited about having some really badass tanks vs. some tin can light tanks. One can level this complaint against games like WitW/E as well, though in those cases you can at least turn the combat detail resolution way up and sit for an hour to see exactly what unit destroyed what other unit. The upshot, however, is that ATG feels “gamier,” but in a good way, like a really complicated and interesting boardgame that does all the work of calculation for you.
At any rate, I like both games for different things, and while I don’t think absolute transparency is necessary for a good game, I do think ATG trumps TOAW with respect to transparency in a meaningful way.