anyone have any experience of using them together? How well does it work? or is it just too much grief?
You don't want to do that. Both ReSharper and CodeRush want the keyboard. Specifically, CodeRush remaps the escape key (ESC) for its own purposes. ReSharper does not like that (note: ReSharper doens't do anything special with the escape key, but it still doesn't like it).
As for choosing between them...they both have their points. CodeRush has better templating and more refactorings. ReSharper has built in unit testing for NUnit, and a healthy set of plugings. ReSharper also has Templates, and a slew of Keyboard short-cuts.