ok, both are C++, that's about all they have in common.
Carbide.c++ is a development IDE that one would use to develop applications in C++ for S60 platform (well, for Symbian OS to be precise), while Qt (
http://qt.nokia.com/) is a cross-platform framework that you could compare to Compact Framework on Windows Mobile (or just desktop .net framework).
so Qt is a set of C++ libraries you can use in your development. it has its own IDE to create and debug projects, but you also can do it from Carbide.c++. Obviously, you need Qt installed and deployed to be able to run your app on the phone.
it is free on S60, but for the other platforms it is NOT. you can use Symbian C++ API from Qt application easily.
Nokia is moving towards Qt recently, so I'd advise using Qt if you target newest and future phones.
