the 8 cores on the 8350 are not by any means equivalent to the 4 cores of the i5, they are nonexistatnt cores, the i5 > 8350, THE BULLDozer series was a momemtous failure.
Although the i5 can beat the fx 8350 in many applications (single threaded workloads) the fx is ideal for rendering and editing, no doubt in my mind the fx will best the i5 in that field, most importantly this is want the OP will be doing. As far as gaming is concerned the fx 8350 will do a satisfactory job compared to the i5.
To the OP, the 6300 is perfect for your needs and budget, it is definitely faster than the i3 in multi-threaded apps such as rendering and holds its own in gaming. It also can overclock pretty well (i have one) but there is just one trade off, It consumes much more power than the i3. But at the end of the day the fx 6300 offers phenomenal value for what's it worth.