Remind me...does Far Cry 3 utilize PhysX? Maybe that's the case.
You probably turned PhysX ON, and since Radeons don't support PhysX by default, you might've got severe FPS drop solely because of that.
You can HPX
Radeons just fine (a cheap GT 640 would be more than enough...or you can use your GTX 560, if you still have it), but by default Radeons don't have PhysX at all, thus switching CPU-calculated PhysX will turn into massive FPS drop at the end. That might be your case exactly...if Far Cry 3 has PhysX settings, try turning them off and see if you get FPS boost. If not, then it's either that PhysX is hard-coded in the game (some games has that), or you really need to upgrade your GPU to a "787x+"-level card.