I don't know what exactly goes into an EE degree but I do know that students take a few Physics courses along with a few calculus courses and I know one of my EE friends is in thermodynamics now. Its not an easy degree by any means.
CS has a LOT of theory crap that's extremely boring + software engineering (boring) + lots and LOTS of writing code (at least at my school). However, the variation of real-world projects is pretty exciting. You could work on anything from web browsers to web development, from Windows to *nix, from folding@home to Counter-Strike, etc. A CS degree opens up LOTS of doors across all industries.