The truth is, the answer depends a great deal on what games you plan to play.
For games that can use 1-4 cores (* Skyrim, Guild Wars 2, Fallout 3, Neverwinter) an i5 will work very well without costing a lot. Great per-core performance yields better results on low core count games.
For games that can use 4-8 cores (* Newer ones like Crysis 3, Far Cry 3, Metro, natural Selection, Arma...etc.) an AMD FX 6300 or 8350 will work very well as they have more cores available. They will also save you a good bit of money.
Honestly, a 3770k/4770k is overkill for gaming with 1-2 GPUs. I wouldn't look at those until you're considering a 3-way crossfire/SLI setup.
So before you decide, look at what you want to play and do your research. Oh and, try to ignore any fanboy hype from either side that you may encounter.
Neither Intel nor AMD is the 'best' in all scenarios.