EzioAs :
envy14tpe :
It will run BF3 on High, not Ultra. I say this cuz you chose a 7870. If you get a 760 you'll run BF3 on Ultra and maxed out(no doubt). Also, BF4 comes out in November so you'll need a little beefier GPU, and the 760 is great for $250 range.
It can run BF3 on ultra.
http://www.anandtech.com/show/7103/nvidia-geforce-gtx-760-review/10
While an Nvidia card is better for BF3, the HD7870 can run the game in ultra, make no mistake
BF3: Ultra, maxed out settings, 1920x1080:
760 gets 70fps
7870 gets 50fps
People want to game with 4xMSAA, not FXAA.
The goal is to reach 60fps, so the 760 clearly does so. And it exceeds 60fps which makes me believe it will handle BF4 much better than the 7870.
Also, I changed the OP's build and included a 760 at the original price of the build.