>>7 This is an interesting point. Does Intel have better performance? Let me say it like this, as a summary: Intel has better performance, but not $50 better performance. You will pay a premium for the brand of Intel when you buy their products.
The FX-6300 is good enough to play games, period. People play Battlefield 4 with it, Crysis, etc. If it really isn't pulling through, you can overclock it since it's unlocked by default. More important is your GPU, which is why I chose the third. The GPU has more impact on your gaming performance than your CPU does, in most games.
I have an AMD CPU, an FX-8350. I have not had any issues with it. I would get better performance with an i5-3670k, but I would not get the $50 better performance it would cost me. Well, it's not worth that to me, anyway. I paid $195 for my AMD, the i5-3670k is
$260. Is that performance boost worth $65? Well, if it's worth it to you, then you can. But, I don't think it is.
tl;dr - Intel will give better performance, for a lot more money. You are correct, it gives better single core performance, less heat, less power consumption, etc. The FX-6300 will not cause issues, it will be the GPU that is the weakest link.