To the intel+amd > amd+amd, no not at all. If you had a more powerful processor then yes.
I've heard that BF4 is buggy in general and your FPS issues could be in part due to that. You could also try disabling crossfire and updating your graphics drivers. In addition you could update your BIOS to the most recent version, and potentially overclock that 8320.
Overall a 4670k provides better FPS than an 8320. In BF4 they're very similar on average, not sure of the minimum FPS of each though. I'd try what I suggested above before buying anything.
I currently have my 8320 overclocked to 4.4ghz and ive updated my bios and my drivers. I have both GPU's overclocked to 1100mhz. Ive even noticed in League of Legends, which i run in borderless (so runs with a single card) i will be at 140-200fps and then randomly have it drop to 38 fps for a second, then go back