It'll run it fairly well. I don't know about fully maxed super settings in really really high resolution, but its a pretty decent system yes. You only need an aftermarket cooler if and when you plan to overclock.
you will be able to run bf3 on high settings 1920x1080 just under 60fps.
Just be cautious that the load times on maps do get quite annoying so maybe purchase a ssd for games if your not to worryed about boot times
and as Nekulturny said if u plan to overclock make sure you get an aftermarket cooler
every thing seams fine you shouldnt have any dramas with this setup
you should get able to get 60 fps on medium settings and around 20-30 on high
I think this would depend on the resolution, as someone else had said.
On 1600x900/1650x1050, we're able to get (XFX Double D HD6870) a constant 50-70 FPS on ULTRA with full AA and textures on single player. On multiplayer however, we had to use High settings with no AA to be able to get a constant 50 FPS (most likely held back a little bit due to our CPU, X4 955).
At 1080p, High settings will yield an average of 50-58FPS on Single Player, and in Multiplayer, I would say around 45-50FPS.
im an nvidia fanboy but the 6870 will do just fine
I used to stick with nvida myself, mainly because I was more familar with their model numbering. Silly reason, especially since the price I paid for my Zotac Amp edition, I could of and should have gotten the 6870.