Hard mode basically increases the overall stats of foes and slightly decreases those of allies, without affecting heroes in any way. This applies to attack, health and armour, but not for speed or exp gained for example. I don't think it affects the mobs' AI/brains about their moves or positions, but it may affect their choice/preference of attacks or attack angles. However, this is difficult to prove theoretically as these function lines are hardcoded.

Another thing to know about difficulty is that it can also change the "reminder" round counters in some missions (the number of round increases in easy mode and decreases in hard mode, to make your moves and attack choices even more crucial).