I also agree that the failings of tactical AI are mostly due to the failings of strategic AI, i.e. army recruitment and the AI not developing its generals. Apart from the often mentioned passive AI, and the overall poor handling of missile duels, I think the AI performs rather well.

With missile duels, the AI is not only passive when outgunned, but it often fails to react when you start shooting its melee troops while ignoring its archers. The melee troops just stand there, allowing themselves to be shot to pieces, instead of e.g. pulling back or taking cover from the fire. This would widen the gap between the AI's missile troops and its main line, but it would also mean that if I want to shoot its melee troops I would have to get much closer to his archers, therefore exposing my own ranged units to heavier casualties.

Another thing is using the terrain better. I don't have any concrete suggestions regarding this, but I really liked how the AI used the terrain to its advantage in STW. Some players may not like the long positioning struggle between the player and AI to see who will get the best terrain, which in STW often meant that troops could become tired while maneuvering around the map, but IMO it adds to the challenge.

With regard to the strategic AI, some of it can be offset by changing the recruitment pools, so that more good troops are recruited while the rabble is unavailable at higher levels of buildings, but I guess improving the AI recruitment priorities would help immensely in this. As for the generals, I don't know how to solve that without the AI cheating (which I hate, and therefore would hate to see the AI getting free troops to "fix" the recruitment), but I do know that facing a high dread/chivalry AI general is much much more fun than facing a captain.