For gaming, the i5-3570K would be the better buy. The hyper-threading of the i7-3770 is unnecessary..... unless you're gaming at 4K, at which point the HT has shown some advantages.
The i5 is unlocked, so you can potentially overclock (if you have a motherboard & cooler that'll support it adequately).
This also assumes you already have a motherboard - I'm thinking this might be an upgrade from an i3? If so, that's fine. If not, you might want to look at newer releases.