I will be gaming at 1080p and I will be doing a little bit of video editing, but mostly gaming. (not planning to overclock anything)
I would try and manage a fx8320 and a 7950 since it really shouldnt be much more than a fx 8350 and 7870xt. Between those two I personally would go with the first since applications I use can make use of the cores but the second should get better fps especally with a good oc on the 7950. So the second one gets my vote for a gaming build.
Depending on your budget, and the rest of the parts you want to use like motherboard and psu.
both choices are good, if you go with the FX8350, then i could higly recommend to go with a decent 990FX chipset board.
i think a FX8350 with 7870XT would be a better combination, for gaming and editing.
But maybe a FX8320 with 7950 would be a nice way inbetween ☺
My budget is really tight, will the 6300 bottleneck the 7950?
no i guess that will be fine ☺
6350 and a 7950 will do nicely oc the 6350 a bit and oc the 7950 a bit and you will be a happy cammper.
Is there a huge difference between the 7950 and the 7870 XT in performance wise?
Not a great deal of difference between the two. Good thing is that if you strike it lucky in the silicon lottery the 7950 will hit 1150mhz+ on the core. I would personally go for a better card over a higher end cpu if its mainly for gaming.