KDE has an awesome amount of libraries and classes to work with. A mass amount of developers that are very talented with their skills. Qt has an advantage over KDE, that is the portability. While KDE4 has started to target Windows, Mac OS X, it is a pain right now. It's only due to the lack of helping hands in these areas. But, this will change the more KDE gets recognised on those platforms and what not.

The many advantages of KDE has others have mentioned already. Is the KDE's localisation, Kross, KTextEditor, KParts, KIO, KActions, KStandardActions, KXmlGuiWindow, etc. I'm happy with my application being developed with KDE. In my honest opinion, would love to see KDE get more used but I don't know much semantics behind it to get that to happen. KDE has made development a lot more easier. Also, the build system is much better than it previously was with Autotools. KDE makes it a lot more easier with CMake. While you can use Qt with CMake, it is a little more difficult due to missing functionality that KDE only has in theirs that will automatically make the Windows icon, installing to specific directories, etc. Let's not forget about automoc.