Firstly, how stable is it?
That's a hard question to answer. It's very rare that we find any application crashing anymore. A couple game companies have put stake in us, and have yet to complain about stability. In our experience, if you have no problems with LWJGL, you'll be fine with jME.
Secondly, how easy is it to learn to use jME if you've got a fair understanding of Java3d- I'm figuring it's probably quite different?
The API is quite different than Java3D. But if you know Java3D well, the overall concepts are the same, just applied differently. Documentation is improving to help with this learning curve (still has a ways to go, but getting there).
Finally what are the main practical advantages of jME in terms of performance and productivity?
I can't really answer that, as I haven't used Xith3D before. I have a feeling that performance difference between the two are minor enough that it wouldn't be a major deciding factor. I think it mostly will come down to community and features. And the speed at which new features are added and bugs are fixed. I would suggest heading to www.jmonkeyengine.com/jmeforum
and hanging out for a bit, see if you like it.