Quote Originally Posted by Caravel
In MTW there was a +1 morale bonus for the AI on expert and a +1 morale bonus for the player on easy. Apart from that there are supposed to be no other bonuses, but this is often debatable.
Actually, there is an old post by a CA developer stating that there is a slight stat increase at hard, and a somewhat bigger one at expert. From a few tests run at hard I can confirm its existence, but it is really very slight, just enough to ensure the A.I. will generally win when all circumstances are equal.