Most games only use 4 cores. You already have 6. Adding 2 more is likely to make no difference to your gaming experience.
My son has a Phenom II Quad core at 4Ghz. My Intel i5 quad core CPU benchmarks twice as fast as his when also running at the same 4GHz speed.
AMD per core performance has not improved much since the Phenom II
To get a better gaming experience, you need more powerful cores, not more cores. That means changing to intel