The i7 is likely to win in almost every situation. If a program is very well threaded then the AMD may be able to keep up, but in 95% of cases the i7 will perform better. Regarding your question, however, in all games the i7 will perform better - just that in ~5% of them the AMD might keep up. The main argument that often goes on is comparing AMD's best offerings to Intel i5 - in the knowledge that the i7 are in a class of their own right now.
Budget is not really a valid argument either, given that you'll need to purchase an aftermarker cooler for the AMD chip (These two chips specifically do not come with a stock option, unless that situation has changed recently?).