I have played both on H and N battle difficulty (campaign difficulty I always have H) and both have its merits:
- on Hard battle difficulty one has to think more about his pre-battle deployment and tactical manuevres during the battle, but eventually it can get too much repetitive as the absolute condition is to kill enemy general as soon as possible - as long as he is around, his troops just will not rout no matter what.
- on Medium battle difficulty one can fully enjoy how beautifully balanced the game is and you can afford to try various semi-realistic tactics and employ various house-rules to spice it up.

Overall I have played and would recommend to use HARD battles with horse-archer heavy factions like Pahlava and the nomads while NORMAL with infantry heavy factions like successors, Gauls, etc. With Romans you can do both. I am now having amazing H/H campaign (ust after Marian reforms) and it great - it keeps the challenge even this late into the game and even my Empire at its zenith soeties suffers horrible defeats.

For campaign difficulty my preference rests firmly with HARD - it is challenging, yet still reasonable, best ballance overall.