Qt is a cross-platform application and UI software development framework for creating graphical user interfaces (GUIs) and multi-platform applications that run on all major desktop, mobile, and embedded platforms. Qt supports a wide variety of development approaches, including object-oriented, procedural, and functional programming styles. The framework is designed to make it easier to develop applications and user interfaces that are optimized for different platforms. Qt includes a large library of widgets, such as buttons, menus, spin boxes, and text fields, as well as tools for creating user interfaces with drag-and-drop features. It also provides tools for connecting to databases and web services. Qt also includes a powerful set of debugging tools, such as a visual debugger, memory and performance profilers, and an application testing framework.
GTK+ is more portable (including embedded systems) and includes more language wrappers than Qt.
Qt is a widget framework, not an IDE
Qt is based on C++ and offers out-of-the-box native support. PhoneGap is a framework based on HTML5.