Crossfire and SLI have massively varying effects for different cards and different games.
Firstly, try fiddling with all the settings on BF3 - change resolution etc etc.
Its possible that something that BF3 is asking the cards to do doesnt work well with your setup and is worsened by the Crossfire.
Second, update all your drivers. Mobo, GPU, storage controllers etc.
If you can try your cards in a friends system. That might help rule out any bottle necks. Though your CPU shouldnt be a bottle neck (as far as im aware).
Also, is this problem JUST experienced on BF3? Have your tried running other games that use the same (or similar) game engine? If its only BF3 try re-installing the game, or Ideally grab a fresh download of it.