BF4 is not a game that is affected by CPU. Don't bother quoting me any sources, my i3 gives well over 100fps and even a weak ass AMD 25w quad core 5350 (doesn't get much weaker) managed 45-80 fps depending on settings.
That's where you couldn't be more wrong. Me switching from a i5 at 4.2 Ghz to a i7 at 4.6 Ghz netted me on average around a extra 20-30 FPS. Was same for GTA too pritty much. I think the CPU does matter.