The GNU LGPL does not force you to share any code, not even when static linking. It is a common belief - you just have to provide a way for the user to link their own copy of Qt with your application and debug it; DLLs already provide this, with static linking you can provide object files.
Qt provides EXTENSIVE features for all supported platforms. The biggest that come to my mind are Qt Concurrent and threading APIs, WebKit, Qt Script and of course, Qt GUI. The fact that C++ is dying is because most people think of C++ as the crap code floating around written using only native low-level APIs, MFC or similar libraries/tools. Qt is a modern and stable development framework that's been around for a really long time. Nokia did not acquire it just for their devices, since their devices are just NOT POWERFUL enough to handle the advanced Qt features, notably Qt WebKit - WebKit itself is really a hog and is not targeted towards embedded development.
Qt is consistently getting more features. For example 4.5 brought a Cocoa port, XSLT, ODF. It also brought a new raster engine that is, get this, STUPIDLY FAST, as well as an OpenGL (ES) 2.0 engine for hardware accelerated graphics. 4.6 has brought an animation framework, a state machine, and an EXTREMELY fast JavaScript engine inherited from WebKit, for WebKit itself and Qt Script - SquirrelFish Extreme is currently the fasted JavaScript engine, beating Chrome's V8; 4.7 brings Qt's version of WPF, called Qt Quick, with a declarative language (QML, based on JavaScript), QtDeclarative module (which integrates with the Graphics View framework and has APIs to bind custom C++ objects to QML), extended networking APIs and improvements to the WebKit module (and updated WebKit code).
What does WPF provide as a browser widget? Trident. Thank you very much, right now Trident is one of the slowest engines in all aspects, though I hear that work is in progress to dramatically improve performance. All a good choice to shoot yourself in the foot when you want to port your software to another program, especially the rapidly growing market of embedded devices - you are basically locked to Windows CE/Mobile, whereas Qt has been ported to Windows CE/Mobile, Embedded Linux, Symbian S60 and Maemo is coming soon. Qt has the most extensive platform support I've seen - see the list in the Qt documentation.
Even though Qt provides some very high-level APIs, it is VERY fast, and when speed is critical, it allows you to go as low-level as you want, potentially even assembly. Alien widgets provide flicker-less fast rendering, however, you are free to request a native widget - just set a flag. For concurrent programming you have threading primitives like mutex, read-write lock, wait conditions, semaphores, as well gradually higher-level APIS - thread pools for example, ending with Qt Concurrent. Signals and slots are an invaluable way to pass data between objects in a thread-safe manner without any locking, relying on the event loop to safely deliver all events and signals.
Qt is extensible as hell. You can subclass practically all classes, and if that way you are unable to perform an operation, you are provided with full source code for all platforms and rights to modify it to your needs on all licensing options. Furthermore, Qt guarantees backwards binary compatibility across minor versions and forwards AND backwards binary compatibility across patch versions (of course, code depending on a fixed bug will not work on versions with the bug; X.Y.Z --> X = major; Y = minor; Z = patch). Tools are also provided to gracefully move to major revisions at your own pace: Qt 4 includes a tool to migrate Qt 3 code to Qt 4 code AND a Qt 3 support module, implementing the whole Qt 3 API (unless the Qt 4 version of the class is fully compatible with the old one), thus your old code is always safe.
I argue that Qt is an application development framework, unlike WPF which is just a GUI part of .NET. Qt includes many non-GUI modules: Core, Network, SQL, XML, Script, and more. All provide both low-level APIs (QIODevice, QTcpSocket) and high-level APIs (QTextStream, QNetworkAccessManager). The documentation is a subjective part, but in my opinion I believe that it is very good and extensive, and when the documentation is not enough, the community is always there to help, as well as Nokia's support contracts.
P.S.: I do not have any .NET experience, I have just stated why I believe Qt is often a much better choice over .NET. There are exceptions to everything and .NET excels in many areas as well; nothing is perfect, you have to pick the right tool for the job. I have tried to list all the advantages of Qt I can think of and why it is a great toolkit. Please consult the Qt documentation at http://qt.nokia.com/doc/4.6/index.html for all the details and remember than Qt is a toolkit, it includes several tools: Qt Creator (IDE), Qt Designer (GUI designer), qmake (build system), Qt Linguist (translator) to name a few.