Qt is... fine... as long as you're willing to commit and use only Qt instead of the standard library. It's from before the STL came out, so the two don't mesh together really at all.
In my experience I've had no issues. Occasionally have to use things like toStdString() but otherwise I use a mix of std and qt, and haven't had any problems.
That's basically what I mean. You have to call conversion functions when your interface doesn't match, and your ability to use static polymorphism goes down. If the places where the two interact are few it works fine, but otherwise it's a headache.
