As I understand, in the EBII framework the AI bonuses become much more important than in the other mods. This is because EBII has very low initial morale for all units as compared to the other mods (I reckon it to be 20-40% of those other mods). I mean, any +1 buff for morale is much more important than in the other mods: moving from 2 to 3 morale has more impact than moving from 6 to 7. The lower tier the units is, the more important the effect is.
A related issue is that the generals' +morale bonuses get also more important. I mean: +1 morale in EBII make a bigger change on the battlefield (again, two-three times, maybe five times, however you'd count it) than the same +1 in the other mods. It should be viewed in combination with fact that the human player is better at sending the general-led armies to the battles and perhaps also at nurturing generals with high influence (a side issue is that it makes it also important to have a precise
information on the true Influence for the player). To some extent it is negated by the fact that +morale bonus (applied to all the friendly units on the battlefield) has been translated in the EBII into +Chivalry (called here "Influence") bonus (applied only to the units in proximity of the general).
Three issues I don't know:
1) what kind of the special bonuses do the AI generals get in EBII - I think they should get it, just to level up the playing field with the player.
2) if the EBII team found a trick to prevent the AI from using non-general-led armies (I haven't seen any mod that would achieve it in the M2TW engine).
3) I'm not sure if all +morale benefits have been translated into +Influence, or there're still some left outside this system (I've had a look at it one year ago, as seen in that linked entry).
Anyway, I personally play battles at H, just for the AI to make up with the described mechanism and with the very basic fact that the player can learn on his own mistakes while the M2TW AI is actually not an AI - in the sense it cannot learn.
And I may be missing something, this is just an outsider view :-)
(besides - thanks QS for the answer)
JoC