No, compilers used in matlab, free compilers like Visual Studio Express vs a paid compiler like Intel XE 2013. For compiling matlab code into distributable binaries.
Matlab code is only compiled by the matlab compiler. The compilers used by matlab are used to compile embedded code (C/C++ primarily). They don't benefit matlab performance in the slightest.
Octave is a Matlab like language which is free. It is the closest you'll get to a compiler/interpreter for Matlab.
With that stated. The question of "which is best" is pretty open. It depends on the platform you are targeting and the code you are targeting. Generally, the Intel compiler produces the fastest binaries for intel platforms. It is usually a wash between GCC, Clang, and VC (Though usually GCC < Clang < VC when it comes to compiler performance).
After that, it is mostly features you are after. Clang and VC are some of the fastest compilers out there with some pretty good error messages. Clang has the best C++ support, but has some pretty bad windows support. VC is integrated pretty tightly with visual studios and is a pretty good environment for C++ development.
GCC hits almost every platform and is pretty ubiquitous in non-windows operating systems.