Yes, the OS can definitely affect game performance. That being said, I have both Win 7 Ult x64 and Vista Ult x64 (with SP2) on virtually identical machines (from a hardware perspective). Performance differences are negligible. Not surprising considering that they use the same drivers, etc.
Win 7 is indeed a better OS, overall than Vista, but it really is just the next iteration of Vista. Tweaked, more stable (at least from a clean, new install perspective), but after you install all bazillion updates and both SPs, Vista isn't as bad as the press made it out to be (and I am not a MS fanboy).
Difference, yes. A huge difference, not likely. Good luck!