I don't think the bonus in combat is that apparent. Just pretend you're fighting generals with a couple stars. The MAJOR difference i've noticed is that on hard the AI will attempt to actually flank with cavalry. On medium it simply frontally charges with cavalry. In the event you are attacked by two armies, the AI will link them up on hard. On medium they usually attack individually.

My medium campaign as Brutii got so incredibly boring that I had to quit. Nothing was challenging and I was SO far ahead in the game that it was just tedious. I'll probably play it a little yet, at the very least to see the senate DoW me.