So, Campaign Difficulty mostly affects diplomacy (bargains, how much factions hate you, how likely it is you'll get war declared on you, and how hard it will be to get any other nation to agree to anything) and Battle Difficulty affects, what, the stats of the AI units?

I'd like to know what is changing when I adjust the difficulty so I know whether it will have the effect I want. If all it does is make weak units strong and gives the AI factions tons of money, I'd like to know that.