I don't think there are any stat bonuses on hard, but i know for sure they get them on very hard. I know on VH a unit of light infantry will decimate a unit of militia, but playing on H i just used a unit of militia and defeated a unit of light infantry with around 30% casualties, which is fair, because all 80 men in a light infantry unit fire at once, whereas only the first rank of my militia fire and then have to reload.

One thing the AI do get on hard is accuracy bonuses to artillery though, this i am positive on.