I do around 90% development on Java EE 6 for highly scalable systems that use mostly desktop and web applications for client interaction (very little mobile requirements yet).
I use Qt 10% of the time, and mostly experimenting on what it would take for me to do the same things in Qt that I currently do in Java, too bad that C++ libraries are still lacking compared to what I do on Java EE (currently I use it for automotive and banking).
I found some replacements for the distributed, highly scalable parts of the systems (ZeroC ICE products, but it's GPL or commercial and quite expensive, and Oracle GlassFish is a lot more flexible licensed), but for deployment and Web communications, still no luck (would be cool to have a good fastcgi or scgi implementation in Qt, I tried some opensource projects but are very old or lacking basic functionality).
Object serialization has really improved in Qt, with QObjects and XML you can go really far, and for Qt5 there's a new serialization module for supporting JSON as well, but still, I think to make it as easy as JAXB in Java, it would take some time and dedication, but with QML stealing all the trolls attention, it's going to be hard to go there anytime soon.
For the desktop client side, Qt is really on top of Java swing, but, there are A LOT of components, both open source and commercial for swing, which Qt is lacking, i.e. a diagramming component, a very-rich-eye-candy charting, an iCal/Outlook like calendar component, a MS Project like gantt/scheduler component (more modern looking, I've seen KDABs and it looks like made in the windows 3.11 days), or text visual diff component (something like that would be useful in Qt, specially for Qt Creator that still has text only diff).