Most current games don't fully utilise four cores yet let alone six cores. The four-core would be the smarter choice particularly if you're on a budget. A four core processor will last you a good while and you can always upgrade later on down the line if you feel it becomes redundant. If you opted for a black edition Phenom II chip then you can easily overclock the CPU. A higher clock speed four core processor would probably match or beat a stock 6 core processor in gaming. 6 cores are only really useful during tasks such as encoding etc where the CPU is really put through its paces. Hope this helps!
Not that they aren't good, its that you do not use 6 cores.
To put things in perspective for you here, you are better off with less cores at a higher clock speed than more cores at a lower clock speed for gaming.
Look into the 955 black edition, I believe its clock speed is somewhere around 3.4 ghz.
I would also strongly reccommend that you take a look into a core i5/p55 build, as you will spend about the same amount of money and end up with an overall faster system. The i5 750 is faster than all but maybe one of the phenoms, and is only $199, plus the p55 motherboards are about the same cost as the AM3 boards, if not cheaper.
If you are really wanting to make an inexpensive rig, you might also want to look into an older AM2+ build. You can get an AM2+ mobo for 80$ or so, put a 940BE in it for about 100$, then spend whatever else you have on the gpu, since the gpu will handle the majority of the gaming workload anyway.
As of now, AM2+ is really the only way you are going to save money by using AMD, or at least save enough money to justify using their stuff.
For a budget gaming build, I would reccomend going the P55/i5 route.
AM3 motherboards are more expensive than p55s, almost to the point that you make up the extra cost on the cpu with the savings on the motherboard.
If you are absolutely dead set on AMD though, I would reccommend a 945/955 BE.
Actually p55 motherboards are more costly than AM3. For gaming all CPUs will be performing same unless you are playing at a very low resolution. AMD 955 BE will be best suited for budget gaming. If u do other things like video encodings, winrar, etc core i5 is superior.
For the saved money u can buy a better gpu. GPU is more important than cpu in gaming