NIB is pretty in-detail on the things in his first post.
I'd like to add:
While AoM has the more "epic" fights (though they are pretty small, compared to RoN or the like), WC3 has one big advantage, which sets it apart into a different category of game for me.
In Warcraft III, many units have irks, powers or other stuff which makes them tremendously unique and entertaining. For example, the Dwarven Mortar team, having the largest AE attack in the entire game, though being a bit less effective at building-killing than siege engines. And they have that funny "MORTAR COMBAT" sound when they are ready.
Night elf buildings can fight and run, Druids are double-units, and so on...
While in AoM, the only really interesting things are God Powers and Myth Units. The problem is that 2/3rd of that, the MUs are stopped by not being designed for being massed.
So i still play WC3, like i play AoM, like i play RoN. RoN is pure Strategy, WC3 is tactics+fun (Dreadlord + Pandaren, the best combo ever *gg*), while AoM is cool for something in between -- though i hate this game in 1on1, when it comes down to pure rushing...
K.Rool,
Master of unnecessary knowledge...