I went from a 6300 to an 8350, then to an 8320. Both the 6300 and 8350 were clocked @ 4.8Ghz. My 8320 is now @ 5ghz. I use an R9 380 GPU.
The 8 cores have better minimum FPS, better physics performance, and way better multi-threading. You will most definitely notice a difference when changing CPU's
Is it worth upgrading right now? That's a good question. AMD's new CPU's come out this year, so while upgrading to an 8350 might be worth it, you could just hold off until the new generation comes out. Of course then you would have to upgrade the motherboard as well..
If you can get a good deal on an 8350 it might be worth it but in all honesty I would probably go with the 480 GPU then upgrade to Zen down the road.
One thing you should know is the 8320 is the exact same CPU as the 8350, just underclocked. You can buy the 8320, overclock it just a bit, and have a CPU more powerful than an 8350 at a lower price.