Actually, I'm of the opinion that you should keep the battle difficulty on medium, as otherwise the AI combat bonuses mess up the unit balance.
However, if you give the AI campaign bonuses instead, you just end up facing wave after wave of full unit stacks, like some kind of greco-roman space invaders game, that's certainly hard but isn't always very rewarding.

The solution, as I see it, is to limit your own 'human advantage' in various ways. One good way would be to have the automated governors manage all your construction and recruitment. That way you won't be able to cherry-pick your favourite units from the roster, and will be forced to fight with whatever you're given (which is a bit more realistic, really). You won't be able to rely on the same tactic over and over again.

Another good rule would be 'no blitzing' - you have to disband your starting army to the point where its upkeep matches your income. No defecit spending allowed.
Other ways of increasing battle difficulty are switching off the minimap, not using the pause button, and not stashing your army in the corner of the battlefield.

I know lots of players have their own RPG-style house rules. Anyone want to share theirs? Adopting some of these would make the campaign more challenging.