I own an Integra Type R and an NSX. I've driven both in quite a few track events as well as on the street (maybe 60 track events in the NSX and 10 in the ITR, in addition to 10 and 30 in my previous GS-R and CRX).
Both cars are exceptional, featuring good power and neutral handling. The NSX is indeed more powerful and more precise, although it never seems heavy at all.
The acceleration on the NSX is substantially faster than the ITR, with most tests showing it a full second faster 0-60 as well as in the quarter mile. Step on the throttle on the ITR, and it accelerates nicely. Step on the NSX throttle, and it goes RIGHT NOW, thank you.
Similarly, the handling and cornering in the NSX is just that much more responsive. The ITR handling is excellent, but the NSX is better. It's a lot easier to hit a particular spot on the track in the NSX than in the ITR.
One noticeable difference between the two cars on the track is the shift points. The stock NSX maximum speed in the first three gears is roughly 40, 80, and 115; in the ITR, it's 30, 60, and 90. On some tracks, I keep the ITR in third gear for almost the entire track, whereas in the NSX I'm constantly shifting between second and third. On faster tracks, I might have the NSX in third and be shifting the ITR between third and fourth.
On the street and for daily driving, the ITR is fun, but a lot more raw than the NSX. The ITR is loud (no soundproofing), and the interior isn't particularly plush.
I disagree with many of ilya's points (sorry, ilya). I think that a stock NSX is every bit as well-tuned for track use as the ITR. I just think that the stock NSX is also well-designed for street use, more than the ITR. You can take a bone-stock NSX out on the track, and it has a suspension that's simply amazing because on the track it holds the corners even better than the ITR (which is no slouch), and yet the ride is also comfortable (not harsh) on the street. There is absolutely no need to upgrade the NSX suspension unless you feel that you must have as little body roll as possible and you don't care about the ride quality on the street. The stock suspension (assuming that the struts aren't worn, which may not be valid on an older NSX that has the originals) holds the corners incredibly well. Even the stock tires are quite competent on the track; although they both come from the factory with the Bridgestone RE010 as standard equipment (as well as, for the NSX, the Yokohama A022H), the tire sizes on the NSX are corner-specific and have built-in bias that works with the NSX alignment for superior handling and grip. (Read more in the "Tire Tech" section of the NSX FAQ.)
While the NSX is indeed heavier than the ITR, it doesn't feel like a heavy car. It feels light and incredibly precise and, overall, just plain more capable. They are both a heck of a lot of fun. When I take people for track rides in the ITR, they're usually surprised that it's as quick and as neutral-handling as it is - but mostly because it's a FWD Integra and they weren't expecting it. When I take people for rides in the NSX, they're usually flat-out astounded at what it can do.
There's no question that the ITR is a more versatile car than the NSX; if I had to have only one car, it would be the ITR. But when I go to the track or to my favorite curvy pavement and I really want to boogie, I'll take the NSX.
Try driving one and you'll see exactly what I mean.