To be honest, i would recomend a 7950. But its one of those things that we wont know how itl run until the beta comes out.
Could run fine on a 7870/7850, or it could run like a slideshow.
Due to the fact that bf4 wont be out till christmas, i would be more inclined to wait for the 8 series amd gpu's and there nvidia counterparts and check then. guaranteed to get more bang for your buck then
Depends on what you want to play BF4 on. 720p, 1080p, 1440p as well as what your expectations as far as graphics go are. Its safe to assume that to get the constant 60 fps your need for competitive shooters your looking at least a 660/7870 on high/ultra mix (assuming its not crazy unoptimized judging from the video its only slightly better looking thank BF3). Then again they were running it on a 7990 so.... idk maybe a $200 card, maybe a $500 card. Way too early to tell but in the meantime get more ram ^.^