In terms of overall gaming performance, the AMD FX-9370 is massively better than the AMD APU A8-6500 when it comes to running the latest games. This also means it will be less likely to bottleneck more powerful GPUs, allowing them to achieve more of their gaming performance potential.
The FX-9370 was released less than a year after the APU A8-6500, and so they are likely to have similar levels of support, and similarly optimized performance when running the latest games.
The FX-9370 has 4 more cores than the APU A8-6500. 8 cores is probably excessive if you mean to just run the latest games, as games are not yet able to harness this many cores. The cores in the APU A8-6500 is more than enough for gaming purposes. However, if you intend on running a server with the FX-9370, it would seem to be a decent choice.
More important for gaming than the number of cores and threads is the clock rate. Problematically, unless the two CPUs are from the same family, this can only serve as a general guide and nothing like an exact comparison, because the clock cycles per instruction (CPI) will vary so much.
The FX-9370 and APU A8-6500 are not from the same family of CPUs, so their clock speeds are by no means directly comparable. Bear in mind, then, that while the FX-9370 has a 0.9 GHz faster frequency, this is not always an indicator that it will be superior in performance, despite frequency being crucial when trying to avoid GPU bottlenecking. In this case, however, the difference is probably a good indicator that the FX-9370 is superior.
Aside from the clock rate, the next-most important CPU features for PC game performance are L2 and L3 cache size. Faster than RAM, the more cache available, the more data that can be stored for lightning-fast retrieval. L1 Cache is not usually an issue anymore for gaming, with most high-end CPUs eking out about the same L1 performance, and L2 is more important than L3 - but L3 is still important if you want to reach the highest levels of performance. Bear in mind that although it is better to have a larger cache, the larger it is, the higher the latency, so a balance has to be struck.
The FX-9370 has a 8188 KB bigger L2 cache than the APU A8-6500, and although the APU A8-6500 does not appear to have an L3 cache, its larger L2 cache means that it wins out in this area.
The maximum Thermal Design Power is the power in Watts that the CPU will consume in the worst case scenario. The lithography is the semiconductor manufacturing technology being used to create the CPU - the smaller this is, the more transistors that can be fit into the CPU, and the closer the connections. For both the lithography and the TDP, it is the lower the better, because a lower number means a lower amount of power is necessary to run the CPU, and consequently a lower amount of heat is produced.
The APU A8-6500 has a 155 Watt lower Maximum TDP than the FX-9370 (though they were created with the same size 32 nm manufacturing technology). What this means is the APU A8-6500 will consume significantly less power and consequently produce less heat, enabling more prolonged computational tasks with fewer adverse effects. This will lower your yearly electricity bill significantly, as well as prevent you from having to invest in extra cooling mechanisms (unless you overclock).