I find that with a single 7950 o/c to 1030MHz, I can play BF4 on max settings, MSAA 2x, 1080p, 40-60fps. You can get these for around $200 in the US now. A single 7970 would be better, more likely to hit 60fps.
With 7950 crossfire, I get a constant 60fps.
The CPU may hold you back a bit, my...