Which CPU is stronger?

Solution
The Intel i5 4460 is 2 years newer than the FX-6300. It has fewer cores, but those cores are far faster. The FX CPU would be a downgrade in every way:

1) Less single-threaded performance
2) Less multi-threaded performance
3) Greater power consumption
4) Lack of newer AVX instruction sets
5) Older platform

You would also need to replace your motherboard with an AMD board to use the slower FX. Better to drop in a Core i7 if you feel the i5 is not delivering the performance you want.
I would say about even in general.
Intel would beat amd in single or dual core calculations which, to be honest, most games still are.
AMD could beat Intel in true multicore performance if software supported all those 6 cores.

Considering it would involve swapping motherboard too, I would not do it.
 
The Intel i5 4460 is 2 years newer than the FX-6300. It has fewer cores, but those cores are far faster. The FX CPU would be a downgrade in every way:

1) Less single-threaded performance
2) Less multi-threaded performance
3) Greater power consumption
4) Lack of newer AVX instruction sets
5) Older platform

You would also need to replace your motherboard with an AMD board to use the slower FX. Better to drop in a Core i7 if you feel the i5 is not delivering the performance you want.
 
Solution
Furthermore, most AMD aficionados don't like to admit that their so called "cores" aren't. They are modules and only the ALU (integer unit) and logic unit are duplicated inside those module. The more important (especially for gaming) FPU for which there is only 1 in each module. So the so called 6 core CPU behaves like a triple cripple under FPU loads.