WinAPI (Win32) is the underlying API. If you code with WinAPI, your programs will work on Windows only.
Qt and wx are higher level libraries that "sit on top of" WinAPI. On Windows, they use WinAPI underneath, but because they are higher level they can use different APIs on different platforms. So code that uses Qt or wx can be easily ported to platforms besides Windows.
Anyway, I've never used Qt but I've heard very good things.
I have used both wx and WinAPI and I can say with confidence that coding with wx is much easier.
Although wx doesn't have as good of tools for developing forms (the resource editor in VS is much better than any of the wx form builders that I've tried). So there's a tradeoff.