Tom's Hardware says they are equivalent to each other and fall in the same gaming tier: »
www.tomshardware.com/rev ··· 6-5.htmlIn terms of 3D Passmark performance:
• FX-8120: 6,660
• A10-5800K: 4,759
The 8120 is $160 at Newegg, and the 5800K is $130 ($115 with money off code). I'd stick with what you have, as in best cases, the 5800K is a side-grade; in most cases, it looks like a downgrade.
If you want a performance boost, consider overclocking the 8120, and put the money towards a good closed loop CPU cooler. There are
dozens of google results for overclocking an 8120--you should be in good hands.
Related question I should have asked earlier--what GPU are you using? Integrated is fine for blu-rays, streaming, and even light gaming, but a dedicated GPU will give you a bigger benefit over anything else you could do for gaming.
Full system specs would let us make a more informed decision.