965 is by far better, the FX are server processors, and if games ARE in fact using more cores(which isn't really true) the 965 still wins by a lot, because the 6300 is 3 Physical cores with 3 integer cores, it's essentially a hyper threaded tri-core. Because each integer/physical pair shares the same L2 and FTPs. It's 6 cores running off the resources of 3.
If you look at benchmarks even the i3-2120 and the 965 BE beat the FX processors even up to 8150 in all but the most heavily threaded of tasks. Plus, the 965 BE is much cheaper, use the saved money for GPU upgrades/future upgrades.
Good luck, btw, 965 OC'd is roughly equivalent to i5 2500k, FX-6300 OC'd is roughly equivalent to BSOD.