If you're looking to do a desktop GUI type of application, then those two are decent choices.
If you have skill in C++ already, then Qt is a natural fit there. Also, Qt's docs are very good. None of the "oh, I was advised to use this class. Where are the docs? What do you mean... go read the source code?".
Gah... sorry... still haven't gotten my extremely bad experiences with Gtk out of my system (years later). ;)
If I were doing a desktop GUI type app again, I'd choose Qt for sure. Good docs, very large user base, actively helpful Community on IRC. (I'm not really a forums guy). Plus, bunches of Qt code (of various quality) on GitHub for getting ideas from.
It sounds like GTK is eliminated too.
What's left now, QT and wxWidgets?