I only have experience with Qt, and can tell you that a problem with the current version is the difficulty in getting a native look on mobile. If you want a custom UI, QML is great, but Digia really need to offer native-looking UI components. They will do this for widget-based UIs on Android in the next version I believe, but no word on iOS.
Native UI goes far beyond the look. Another concern is accessibility, especially for blind users. Non-native UIs can be accessible, but only if the toolkit implements each platform's accessibility API, and gets the implementation right, which seems to be very difficult. (For example, last time I checked, Qt's implementation of the relevant accessibility APIs on Windows was deficient enough that the TeamTalk voice chat client offers a "classic" MFC-based client specifically for blind users.)
I don't have direct experience with either Qt on mobile platforms or Xamarin, so I can't provide exactly what you asked for. But I can provide a considered opinion.
I strongly recommend Xamarin over Qt, because even if you use Xamarin.Forms, you'll be using the actual native UI on each platform, not a mere approximation. So your app will be more true to the native look and feel of each platform. Moreover, it will be accessible to users with disabilities, especially blind users, as long as you don't implement any custom widgets of your own. (If you do need to implement custom widgets, you'll need to implement each platform's accessibility APIs as well.) True, these users are a minority, but if you can make your app work for them without considerable extra effort on your part just by building on the right foundation, then that's a win-win situation.
Qt may offer the promise of "write once, run anywhere," but IMO, that should be more like, "write once, be inferior everywhere."
