Intel's CPUs have better IPC performance than AMD CPUs / APUs. That is the main reason why Intel CPUs are better. IPC stands for Instructions Per Clock (or Cycle). In essence it basically means that for every 1Hz an Intel CPU can process more instructions (or data) than AMD can. This explains why if an Intel and AMD CPUs are both clocked at the same speed, Intel's CPU wins. As an analogy, suppose person #1 can type 60 words per minute, and person #2 can type 55 words per minute. Assuming absolutely no typing mistakes, who do you think can finish typing a 1,000 word essay?
Extra cores found in AMD CPUs and Hyper Threading found in Intel's CPUs can improve performance, but only if they are taken advantage of. As stated above, AMD FX series CPUs are not "true" 8 core CPUs because the Bulldozer and Piledriver architecture is built around a modular design. There are actually two cores per module, but each module only has one FPU (Floating Point Unit), therefore if one core is using the FPU, the other core must wait. Therefore, the actual performance is less than a "true" 8 core CPU. Also, just because there are 8 cores hanging out, that does not mean a program will all 8 cores. The program must be designed to use those cores.
Programs capable of using more than one core are called "multi-threaded" programs. It is technically possible to design all programs to use 8 cores. However, doing so takes more time to design and test the program, that means more money for development. So if you don't mind potentially waiting longer for a program to come out and at the same time pay more money for it, then I'm sure software companies would be willing to design such programs if it makes sense. For example, designing a simple calculator for basic adding, subtracting, multiplying and dividing operations that can make use of 8 cores is a total waste of resources.
The vast majority of games use only one or two cores. Combined with Intel's higher IPC (compared against AMD's FX CPUs), their CPUs generally perform better in games at can make use of a faster CPU. Skyrim is a good example of a dual core capable game that benefits from higher frequencies so if you can overclock your Intel / AMD CPU by 500MHz above stock speed, then you will see a performance difference. However, many (if not most) games are not really dependent on the CPU as long as it is not slow enough to bottleneck the graphics card. Crysis 2 is a good example of a games that does not care how fast your CPU is as long as it is not holding back the GPU. At 1920x1080 resolution with whatever highend graphic card used for the review I read sometime ago, Crysis 2 did not care if you were running a Core i5-2500k at stock speed or at 4.8GHz, the performance increase was only 1 or at best 2 extra frames.
There are a decent number of games that can make use of 4 cores, but in comparison to the number of games capable of using 2 (or less) cores, it is miniscule. Of course, if you know the games you will be buying can make use of more than 2 core, then it makes sense to buy a quad core CPU. The only game I can think of that may be able to use up to 6 core is Battlefield 3 in multi-player mode. But that game is the exception, not the rule.
Intel's Hyper Threading technology (HT or sometime called HTT) are virtual cores. Unlike the physical cores in AMD's FX CPUs. Generally speaking having physical cores is better than having virtual cores; even if those physical core are sharing resources. Basically speaking, HT works by searching for a core that is simply idling, if all cores are 100% busy, then HT just waits... once a core becomes available HT uses it to process another thread (stream of instructions / data). Technically speaking HT can ensure all 4 cores are full utilized as long as there are some programs running that needs to process data. This is a very simplistic description so take it with a grain of salt.
The problem with HT is similar to AMD's 8 core (and 6 core) CPUs. If a program is not designed to use HT, then it won't. Probably the most common program at almost everyone uses once in a while that are both multi-thread (using all or most of the available cores) and HT are file compression programs like 7-Zip and WinRAR. Some video encoding programs and video codecs can make of use multiple core and HT as well, but not everyone encodes videos. However, games are not designed to make use of HT. Actually, there was one game that came out in 2011/2012 that was designed to use HT. It was some space combat game that simply bombed. I think the best review it got was something like 4 out of 10; pretty bad...
Anywaste... in the end games generally perform better on PCs with Intel CPUs compared to AMD CPUs if they are CPU bound (dependent). That's assuming the same clockspeed. AMD CPUs would need to be clocked higher to provide the gamed level of performance as Intel CPUs in CPU bound games. Different games have different CPU dependencies.
For a pure AMD gaming rig I would probably go with the quad core FX-4320 which has a clockspeed of 4.0GHz/4.2GHz. It is also pretty easy to overclock as well. Sure, it does not have 6 core or 8 cores, but it also produces less heat and consumes less electricity. If you are a huge fan of BattleField 3 and plan on buying other games based on the Frostbite 2 engine, then the 6 core FX-6300 would be preferable. However (at least with BF3), the game only uses more than 2 cores in multiplayer mode.
So what about the 8 core FX-83xx series? For a pure gaming rig I think it makes more sense to get the FX-4xxx or FX 63xx CPUs. The 7th and 8th will likely never be used in games. But if you do other CPU intensive things like encode video in addition to playing games, then yes for I would recommend going with one of the FX-83xx CPUs.