The Federation would definitly win. The Federation is just better then the Empire in every way.
Ask a question like this on a ST or SW site or ANY site for that matter and you will get a bias answer/argument.
Galactic Empire vs. United Federation of Planets? Galactic Empire just for sheer numbers. HOWEVER: The Galactic Empire would have a VERY difficult time getting past the rest of the Star Trek universe. ie: Borg, ect.