I took the FE exam roughly 10 20 years ago, so I'm not sure how relevant my experience is. I took the test just after they changed from allowing you to bring any and all reference material, to only allowing a reference booklet they provided.
I noticed that the supplied reference book had all the information needed to answer almost all of the electrical questions, but the mechanical engineering information was not sufficient. Me and several others who took the test seemed to think it favored mechanical engineers.
There were questions about basic stuff, engineering economy, partical dymanics, statics, etc.
I passed the test, but I never went on to take the PE test. I'd imagine I've forgotten so much now that doing so would be quite the ordeal.
EDIT - crap, time files by. I had no trouble typing "10 years" when it has actually been 20.