I have just made this switch and realizing there isn't much solid information one can grab on google concerning this particular switch.
...yes there is a big difference.
Especially in the way of anti-aliasing where as on the 5850 AA means a massive hit to frame rate, with the gtx580 it doesn't seem to phase it at all.
I did a quick run through several games the largest and most immediately noticeable difference was in batman arkham city and SW:TOR.
The 5850 really struggled to get BAC going with the settings cranked up.
I got slow downs and strange behavior when using the ati card, with the nvidia card I've cranked everything as high as it can go and it just keeps going.
Also bear in mind I had my 5850 overclocked and I'm running the gtx580 at stock.
There is a general added crispness and the panning jitter I always got to some extent with the 5850 is also gone.
Mind you I'm speaking about most of these things on a level only a enthusiast would probably even notice. Except BAC where the difference was just mind blowing.