There is little doubt that Intel's current CPU architecture has better performance per clock that AMD's FX. But it's not that simple. AMD give you more clocks 4.2 vs 3.3 and that's just enough to pull even with the i3. Plus you can over-clock the AMD if you like which just makes it more fun. The AMD uses more juice, but in a gaming rig, it's not a big deal.
Your budget comparison is also a little unfair. The AMD system is built, has Windows 7/8 and a much better motherboard supporting USB 3 and SATA 6, features I would not exclude on any build now, and comes with the support of the builders guarantee.
In terms of future upgrades the AM3+ platform will get piledriver and steamroller CPU's, which based on the performance of the new trinity (piledriver core) APU's will bring AMD much closer to Intel's performance.
In truth for gaming you cannot really go wrong, Intel will give a bit better performance, AMD have to compete on value and features, either is fine, so long as you have a fast quad core, it's your GPU that will define the performance of your games.
I have an old X6 AMD, I built my wife an i5, both with ATI 6870's, both perform about the same.