Here's another interview with the cast of the SatC movie. I'm only quoting one response Chris Noth made because I really like what he said about Criminal Intent. Full article at countingdown.com.
Q: How is it different shooting Sex and the City and Criminal Intent? (Chris Noth joked about denying Law and Order; saying about Criminal Intent "we're different, we're better, we're on USA")
A: Well, there's estrogen and there's testosterone. There's fashion, and there's death, there's cheap suits and great suits and both great crews and then really different kinds of writing. I would say that Criminal Intent, I think we've doing the finest work since I've ever been on Law and Order; I think the shows are phenomenal. We have a small audience on USA but on my side, because I don't watch the other show (laughs); but I know that with my partner Julianne (Nicholson) and Alicia Witt, that I can't complain. I think the material is fantastic; it's just harder to do because it's procedural, and its story and it can be very argues. Once it's put together, I'm usually pretty proud of it. Sex and the City is, you know, it's a gorgeous piece of work. Writing like that uplifts the actor, it uplifts you and it makes your job a lot easier and a lot more fun.