There was an excellent post about this, but for the life of me I can't find it again, nor tell you who did the research in the first place

Basically, in VH difficulty, relations default to Abysmal over time if you let them be (ie you don't give money/maps/regions to get them back up all the time). In M they default to neutral, in Easy they default to Good. Of course, Abysmal relations generate completely insane diplomatic demands and suchlike.
Also, being one of the top 3 factions worsens your relations with everyone. Attacking a faction worsens your relations with every other faction sharing the same faith.

Not sure if the relation thing is factored in strategic choices by the AI though, BUT the researcher also stumbled upon a disturbing thing : if the player is not at war with anyone for a number of turns, it automatically triggers an AI attack, presumably to keep the player on his toes all the time.

The "peace length" varies with difficulty as well : in VH, 4 turns of peace with everyone triggers aggression, in Medium it's 10, in Easy 20. So it seems that, if you want to keep your direct neighbours relatively quiet and sane, you need to have a "pet war" going on somewhere (don't know if the war needs to be active or not though, that is to say, I don't know if those turns of peace are "turns without any battle" or "turns in which your faction is not at war with another". But picking a hopeless, non-Christian scapegoat and blockading one of his ports all the time seems to be working for me.)

Knowing that has conforted me in thinking that M/VH is the way to go, not VH/VH.