We usually play with friends on all random (faction, hero, starting bonus, and map), on impossible difficulty, without any restrictions in the rules.
Under these conditions, the strongest faction is Conflux, and after that, it's hard to say, except that Inferno is the weakest (its only chance is to quickly find a scroll with Armageddon, then you can win with Ifrits).
As for personal preferences, I don't like Necromancers (it's just boring to spend the whole game accumulating skeletons, trying to prolong it as much as possible) and Barbarians (it's just a matter of style, I've always preferred hero-mages).
I enjoy playing with all the others :)