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 3570k o/c to 4.4GHz runs at 70-90% @ 60fps. With Vsync off, it hitting 70-80fps, but if I don't o/c the frame rate drops, so it's definitely CPU limited. Plus the 7950 crossfire are only at 50-70% usage @ 60fps.
At 1080p, it never takes more than 2GB Vram. Which is annoying as the recommended Vram is 3GB, which made me buy AMD instead of Nvidia, but I guess that was the idea. Unless they are saying typical gaming is at greater than 1080p, but that goes against 98% of games using 1080p.
There's a quick way to check greater than 1080p, just increase the rendered resolution (in options) to > 100%. eg setting it to 200% = 4k res or 4 x 1080p monitors. At this res, it still only uses 2.8GB Vram (MSAA x2).
Mind you, this is all pretty moot, as the game has so many bugs, you'll be lucky to play it without the server refusing connection, the game crashing half way through or failing to load the next map.