In most of the games you listed, Intel CPU's will be significantly faster than competing AMD ones.
The difference can be as much as 25%.
What this basicly means is that if you're getting 50 FPS with the AMD you'll get 60 with the Intel.Assuming you're using the same graphics card.
But then, when you consider the price difference, you can buy a card that is 20% faster with the AMD CPU and get the same performance.
I made you a combination of parts (half build) which is pretty much the best you can afford, assuming you're not going to overclock.
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor ($149.99 @ Microcenter)...