http://www.tomshardware.com/reviews/fastest-graphics-card-radeon-geforce,3085-7.html
The GTX 560 is at the same tier level as the 6870 so there is no advantage there and that means it would come down to drivers , which one produces the better and more frequent driver updates. In that situation I would lean towards Nvidia and when it comes to BF3 the Nvidia drivers do perform better than AMD's. You should also look at what other games you play or plan to play to see which company puts out the better drivers. Nvidia does seem to do well with the new games when they are first released , thier drivers are usually ready to go and AMD seems to lag behind a little but they do catch up.
If you already had the Gigabyte 560 , why did you pick up a 6870 and not another 560 to go with SLI.