I would tell you go AMD, for under $600 you can only go with an i3 and for gaming i would say go with the AMD FX-6300 for $140 you cant go wrong with that CPU i use it in my Budget and have it @4.8GHz and i love it, plus the FX-6300 kills all i3 intel has to offer . Im just telling you to go with something you wont regret later on, FX-6300 6 cores, i3 4 threads from a dual-core!!
Which platform to go for entirely depends on your budget and usage. Your after gaming performance and on a $600 budget.
Given your low budget, it makes sense to go AMD as they offer better performance at the price-point your after.
If you had a bit more cash, then it would make sense to go Intel, because above $200 they pretty much dominate.
If you were after multi-threaded performance on a budget, again its best to go AMD until you can afford to spend $300+ on a CPU. If you can then its better to go Intel.
Of course, whats true now may not be true later on. Who knows, Steamroller might be the revolution AMD desperately needs and Haswell could fall on its face.
So it depends when you are buying, for what purpose and what budget your at. Its not as easy as saying that one is better than the other.
o, if you have a limited budget, go for amd, the FX 6300 is good enough, or you can also buy the 8320. for Intel, you can buy the i5 3330k. both are great. but processor is only 30-40% factor for gaming. spend more on the graphics card. AMD radeon hd7770 is good. or the NVidia 650 or 660 ti.
in all seriousness however, it depends on your personal needs. as powerful & shiny as the intel hex i7's are, they are just overkill for the vast majority of users. figure out your needs & budget; base your choice on that.
If you had a (let's say) $800 to $1000 budget we could argue on this. Since you are building a budget gaming rig, any more dollar you can put in GPU is more important that the amount you put in your CPU. Just keep in mind... Also at this price point, it is vague if you should expect future proofing one or not. I wouldn't. I'd get a fx 6300 (like mentioned before) and a GPU like HD 7770 / GTX 650 Ti / HD 7850 or even a GTX 660 depending on the bank. Peace and cheers