I can't answer the "versus Kubuntu" part so I'm not sure how happy this comment will make you, but I've been using Fedora KDE since fall 2009 and personally haven't had any problems with stability.
In general I'm quite happy with how Fedora distributes KDE. They don't patch it very much and leave it mostly vanilla, focussing their work on system integration instead of modifying to differenciate their offering. That's reflected in the work they've contributed upstream, like PolicyKit support or PackageKit integration for widget installation in the desktop shell (for automatic dependency installation). Nothing flashy, more under-the-hood work, but somebody has to do that as well.
Their KDE packaging team is very competent, and the leader, Rex Dieter, is one of the nicest fellas I've encountered in FOSS. Others can be a bit stubborn at times, but are still useful and supportive, making #fedora-kde on Freenode one of the better user support channels I frequent.
Very nice for me as an upstream developer is also that they explicitly strive to support KDE development, so they will generally swiftly package any new dependencies required by KDE's development branches.
I tried Kubuntu about a year and a half ago, so it might have changed in the meantime. What I remember is just a lot of little annoyances and things not working; however, since this was my first Linux box, I didn't really know what I was doing. I also remember that KDE distinctly felt like a second-class citizen.
For a while, I used OpenSUSE, which has great support for KDE--I was very happy with it but decided to try something new on my newest laptop.
Now I use the Fedora KDE spin and it's awesome--almost everything works exactly how I want it, and everything else is configurable. I've also had no stability issues with Fedora 16--I had some graphics problems and small annoyances with 15, and they all seem to be fixed.
As far as packages go, I've missed nothing on Fedora--they even have a decently recent version of the Haskell problem in their repos. Emacs mysteriously came without Tetris, but that's an issue I can live with :) I would definitely recommend Fedora over Kubuntu for KDE.
Also, the newest version of KDE--regardless of distro, I think--is a nice improvement over older versions. One think I suggest is switching out the default menu for Lancelot, which I find much nicer.