I am trying to compile qt, and am faced with two choices whether use MinGw or Visual Studio compiler? What is the difference between them, and are there any advantages/disadvantages of using one or the other?
They are both fine tools. The important thing to know is that they don't necessarily play well together. That is, as you link libraries together, they must all use the same tool chain. For this reason, in my opinion, it is better to use the Visual Studio compiler (MSVC), as it is the "first class citizen" on Windows; the others are treated somewhat as second class.
What I mean is that you can pretty much count on third party libraries being available in binary form using MSVC, or at least build instructions being available using MSVC. We had lots of problems with third-party libraries not being able to build in MinGW or having nonexistent build instructions and having to do a lot of manual Makefile editing, etc. You are much more likely to have things "just work" if using MSVC.
That is just our experience (we started with MinGW); your mileage may vary.