I know for certain 7 does, in fact it's been more stable for me under Vista than it was under XP.  I can't imagine why 6 wouldn't, in fact I haven't had trouble with any of the apps I used to run under XP with Vista.

Now, a word of caution, not everyone has had such luck with Vista, it can be a bit finicky about the hardware your using and if you don't at meet or exceed it's minimum system requirements you might want to reconsider installing it.

Also as with any windows based operating system, your best bet is to wipe a partition and do a clean install, trying to install over a different version of windows all too often results in problems, particularly in the stability area.

So if you are going to give Vista a look you'll want to backup your files and do a clean install for best results.  Personally I'm very happy with it, but mileage does vary - a lot of other folks were not happy with it when they installed it.  

Hope that helps..

Stepdad