The fx 8350 is better at everything except price and power consumption. And since it's an octo core youre going to see really good performance in video editing. Its worth the price tbh, get a decent cooler and overclock it to make it a beast for it's price
Well, for games that only use one or two cores they will be the same. The 8350 may be slightly faster do to higher clock speeds but thats it. Some OCing on the 6300 could get you there. For productivity and other multicore work the 8350 will be better.
It will work, you just shouldn't expect good overclocking performance. Some of the 970 motherboards can't even handle a full load on the 8350 at stock clocks and will throttle, this may have been fixed with some of the newer board revisions though.
The power connector and presence/absence of VRM heatsinks are what make the difference in OC'ing.
I can attest to the fact that a mobo w/ a 4-pin power connector will throttle an 8350 even at stock speeds and sometimes even crash. I just switched from an Asus M5A97 LE R2.0 to a Gigabyte GA-990FXA-UD3 for this very reason (and to finally be able to OC, a must for 8350's). Just look for a mobo with an 8-pin power connector and VRM heatsinks, I believe the MSI 970 gaming mobo mentioned already has both of these features.
The 970 chipset is not going to be a bad choice, if you plan on overclocking make sure to find ones with a decent power phase design. The only issue you may come across is the bios revision, which would require you to flash it to the latest version (or at least what ever one supports your processor). This board "Gigabyte 970A-UD3" is actually pretty decent, has the same power phase design as its 990fx counter part. Also it seems to just have a better design than most am3+ boards.