7. H is the hardest difficulty for the campaign map. I'm fairly sure VH campaign is somehow bugged and the AI doesn't receive the bonuses it's meant to. As for the Battle difficulty, nothing affects how the AI actually fights. The only thing that changes is that the AI gets bonuses of +3 to attack, defence and morale on Hard and +7 to the same on Very Hard. Medium gives no bonuses to either you or the AI so that's really the fairest and best way to go in my opinion. Otherwise on VH or H you might see your heavy cavalry get absolutely destroyed by low-level peasants and militia.