Well, other than the fact that you'd be going against more people yet still have teammates, there wouldn't be much of a difference in a 3-team game considering you're still killing anything that moves without a blue nametag floating above it. Unless it's capture the flag, but then that's going to be chaotic as hell.
But that would actually be kind of fun...
You could get two flags at once lol.
Oh, but then two teams could conspire and gangbang another team. :/ 12 vs 6, or 10 vs 5. Uncool, man.