AMD CPU with roughly the same power as an i3-4150

not entirely true. Well threaded games the FX 6300 will be clearly better, poorly threaded games the i3 will be in front.

Between the two, the FX 6300 is better.

Of AMD FX's, I'd grab a FX 8320, solid CPU for the price. To me, getting an i5 4690k is a far better choice. The FX's excessively high cores is something to take note of, it's just like an intel CPU with hyperthreading and labelled to have that amount of cores, whereas intel don't label the hyperthreaded cores as 'actual' cores.
 
The FX6300 is a solid all round CPU.

However single threading the I3 will just do better, since most games do not run on more than 2 cores, i find the I3 a better option, but thats because I enjoy Guild Wars 2 and Planetside 2, both CPU hungry games.

BOth will serve you well anyway.