I generally play Prince (yeah, I know, I'm a wimp - but I hate micromanaging at higher levels), Large, Pangea/Erebus maps. Occasionally I overload the number of AI's.
All these are based on score levels toward the endgame; in addition, I play more of a builder style so this is with minimal player influence.
Top: Elves (of whatever kind)
Vampires (God, I hate Decius)
Elohim
Clan
Bottom: Bannor
Grigori
Mercurians
Infernal
Kurios
Middle: Everyone else
Of special note: The Doviello seem to be a hit-or-miss in power. Either they conquer a couple neighbors (in congested maps) and become strong, or they head straight to the bottom. Also, the Bannor seem to vassalize in every single game, and always to some evil guys.
Of course, starting position has the most influence on points standings.
I would like to note that I don't really believe that this power imbalance is completely caused by the individual civilizations' benefits and limitations. Rather, the AI is only good at playing a few styles. For instance, the AI does very well with the extra population of the Calabim, but cannot cope with the late starting civs. The exception is the Bannor, who have no special tricks for the AI to misuse (and, in fact, are as "vanilla" as FFH gets), and therefore really shouldn't be at the bottom all the time.