A 6300 is pretty much an 8350 with 2 less cores and at a lower clock speed.
In theory a 8350 should perform slightly faster per core due to the higher clock speed, and even faster if you're going to use all 8 cores (which you won't if you're gaming).
But the 8350 just isn't really worth the money since the difference will still be pretty small in nearly all games nowadays, the 8350 would be better if you're doing something which would benefit from the 8 cores, but again, you're not.
The 6300 is a much better option for you because it's much more suited your current graphics card, and even if you upgraded to something like an R9 280x in future, the 6300 would still be fine, you can always overclock it if you want to reach the clockspeed of the 8350.
But, again, list your FULL specs so we can give you a better answer.....