Generally speaking the AMD processors are going to give you better price-to -performance. The I7 will give you better performance-per-watt. Also it will all depend on what games that you are playing and your over-all gaming goals. If you want to push the ultimate limits of gaming performance go team blue. If you want to just get your feet wet and learn on the cheap go team red.
The i5 is probably your overall "best choice" for gaming...BUT, since the graphics card is usually more important to determining final performance in most games, a weaker [AMD] CPU with a stronger graphics card will often outperform a stronger [Intel] CPU with a weaker graphics card. Check benchmarks, because there are a few exceptions, particularly where minimum frame rates are concerned. In general you don't want to use too much of your budget on the CPU if that won't leave you enough for a decent graphics card. For a gaming built, try to get at least a GTX660 or R9 270 / HD7870.