AMD's hexacores perform worse than a Phenom II X4 and even worse vs a i5-750 in gaming.
Hence, it's not worth it. For the budget you can easily fit in a 5870 and x4 which will work fine. However, the i5-750 is a better processor and still fits in budget.
The budget does not fit a 5970 and I don't bother with the GTX 480.
I am really unimpressed with the hexacores atm, so defo go with the Phenom x4 955 or better yet, go with an i5 750, way better gaming performance, and the i5 750 is really easily overclockable if you want more clock speed
a) Overclocking is an art, not a science. You aren't guaranteed any specific results, as it still depends on the specific physical chip you get, not just that you got Model X + Cooler Y.
b) Very few games currently use 4 cores. Mainstream computers are still being sold with 2 cores, and game companies aren't going to bother requiring 4+ cores until well over 50% (probably more like 75%) of the market has 4 cores...which will be at least another 2-3 years. Even then, most gaming is much more heavily dependent on the graphics card rather than the processor. Finally, not only does it make business sense to keep core number requirements low, there's a limit to how much gaming can be parallelized.
Games are very poorly threaded. The part of gaming that is well threaded, the graphics portions, is handled by the GPU, which already have hundreds of cores.
In gaming, the most CPU intensive task is AI. AI, by definition is not a parallel process. It is extremely difficult to thread AI. Most games that are "multi threaded" actually keep AI on 1 thread and throw the rest (minor far less intensive stuff) on the other.
Can you design a game to utilize 4 or more cores? Sure, you can throw all the CPU non intensive calculations onto their own threads, but until someone figures out a good way to thread nonparallel computations, the performance increase will be minimal, as the hard work is still restricted to 1 thread.
This issue has been stumping programmers for decades. There are ways to do this in specific situations, but no general solution yet. A general solution allowing infinite threading of nonparallel calculations would be the programming equivalent of finding the cure for cancer, noble prize stuff for sure.
Basically think of it this way. On a math exam you have a 3 part question in which the answer to part each part depends on previous answers. IE
A. Add up 3 and 5.
B. Use the answer from part A and divide by 2
C. Use the answer from part B and triple it.
what is the final answer?
This is the type of thinking AI requires. Threading this is the equivalent of calculating the answer to A, B and C simultaneously. It's not impossible like the mathematical equivalent is, but it's not easy.
For this reason, more than 3 threads has very little benefit.