Qt (the "t" is not capitalized to avoid confusion with QT, quicktime) doesn't really integrate spectacularly well with any IDE. This is due to the need to run the uic and moc tools before passing any actual source to the compiler. The best bet for simple programs is usually to use qmake to manage the process. It can help to have a highly configurable IDE like CodeBlocks, though.
Comparing Qt 4 and wxWidgets 2.6, the compiled libraries are both highly modular and about the same weight (approximately 8 MiB for ALL of the modules and around 5 MiB for just the core components). From a performance or distribution perspective, therefore, you're not going to see much difference.
Qt takes a bit longer to compile and has a more complicated build process for all but the simplest applications. The API is solid, and there's functionality for nearly anything you might want in an intermediate level program.
wxWidgets is more of a complete wrapper than Qt. It uses GTK+ on Linux/GNU, win32 on Windows, and Carbon on Mac OS X. Qt, on the other hand, tries to avoid using platform specific API when possible. It does integrate with a few components, like the drawing mechanisms and the Input Method Editors, though.
You should try building a small application with both to examine their APIs, their event handling mechanism, and build processes.
