Ambient remnants after noise reduction

You have to bear in mind here that Audacity's NR is pretty crude. Mainly because it only works at one - very low - FFT window size. Audition's NR on the other hand, is a lot more flexible - it can use multiple FFT sizes and there are considerable benefits to be gained from using them. Audacity's NR is a bit of a one-trick pony - it works on speech reasonably well but on music it really isn't very good at all, simply because of this lack of flexibility.

What appears to happen is that the Audacity NR acts almost like a gate with speech, which is why it appears to cut off cleanly. What this does with music is remove a lot of lower-level artifacts that really, you want to keep.

So what is it that you have to do in Audition? The basic rule is to use multiple passes, at different FFT settings, and don't take too much noise off in a single pass. Personally I start with a high FFT setting, but I wouldn't take more than about 6dB of noise off (typically) and this avoids the build-up of artifacts. Then do another pass, similarly, at a mid range setting, and the last one at a low setting. The important bit at every stage is to listen carefully to what's happening, and always err on the side of caution with it, especially whilst learning what it's capable of. Yes, there's a learning curve...

And yes, it's more complicated than Audacity's NR. But it would be - it's a professional product that is designed to work on a lot of different sources, not just speech.