The 6300 uses the Bulldozer (Zambezi) architecture, and the 8350 uses the Piledriver (Vishera) architecture, which is newer and better. So the difference is not just in number of cores and clock speed, but also in a better architecture. The AMD FX 8320 is $40 cheaper than the 8350, has a lower clock speed, but still packs 8 cores and the better Piledriver architecture. It is also unlocked for an overclock. That is likely your best choice.
Edit: Actually I'm wrong about the difference in architecture. Somehow I got confused. The 6300 also uses the Piledriver architecture. So, the 8320 may still be worth the difference in price to get you to 8 cores.