Which AMD processor is the better?

Solution
Yes. Ok. If the GTX970 is a gift, I can understand now.

At school we have run the Intel Pentium G3258 and overclocked it on the same system as the i3 4130, i5 4460, i5 4590, i5 4690K, Xeon 1231v3, and i7 4790K. The all fit in the same LGA1150 socket.

For a real budget AMD system, I would look at the Athlon X4 860K
The FX6300 is better, but neither is ideal. Are you making this choice for budgetary reasons or because that's the motherboard you have? If you have a motherboard, what make and model. It may not be able to run a FX6300 well.

The advantage of a 'shitty i3' is that it can be replaced later with a great i7, an option that is not available to you in the FX series.

You choose to afford a GTX970 that those CPUs will not be able to drive to the best effect, but choose not to afford a CPU that will drive it?
 
Yes. Ok. If the GTX970 is a gift, I can understand now.

At school we have run the Intel Pentium G3258 and overclocked it on the same system as the i3 4130, i5 4460, i5 4590, i5 4690K, Xeon 1231v3, and i7 4790K. The all fit in the same LGA1150 socket.

For a real budget AMD system, I would look at the Athlon X4 860K
 
Solution