With AMD FX 6300 and FX 8300 processors and basically any game out there is not a noticeable difference according to what i have read. And based on my limited experience with AMD,; higher Clock speed is more beneficial than 8 cores over 6 cores and 4 cores. That is just how D3D11 is and will be. The FX6300 is just as good as any other AM3+ Socket CPU for gaming . and can Overclock to decent numbers.
What role does your motherboard play? You mentioned a replacement...
EDIT , NOTE: BF4 would be the exception as far using more than 4 cores. Bf3 is said to use 6 cores as well.