Two factions is the majority approach for MMOs that have them, and it's easy to understand why. We can comprehend an "us vs. them" mentality in almost every walk of life. If you're not with us, you're against us -- that sort of thing. Two factions draws a line in the sand and requires little explanation for people to understand that one side is naturally better than the other.
Three factions, on the other hand, is a godsend for PvP in particular. By having a third faction, it's much less likely that one side can dominate the battlefield eternally, as the other two sides can team up to put an end to that nonsense. Three factions also offers more variety and arguably stronger factional identities.
So what say you? Two or three? Cast your vote after the jump!