Really depends on what you're playing. Most games will run great with it, especially if you can overclock it. Maybe not the absolutely highest settings in some games, but definitely very nice.
Some games are very CPU intensive, or heavily favor a particular brand or type of CPU over another. For example, the new SB i5/i7s are much better than even a highly clocked Phenom II X6 on Skyrim. I've seen both in person. Skyrim is noticeably more fluent on the new 2500k (stock clocks) vs a highly clocked Phenom II X6 (I don't remember the specifics). The GPUs in both computers themselves could pretty easily handle high or ultra settings (5970 should have no problem at all), and it was amazing how much smoother the 2500k was at all times. The graphics were even set higher on the 2500k machine. Of course, I've heard this is because Skyrim does a lot of the shadow work with the CPU. Still, there are times in which, yes, your AMD CPU will be a problem. But apparently you just upgraded! I think it will be worth it overall and in the long run.