anyone have any experience of using them together? How well does it work? or is it just too much grief?
I use both tools succesfully. Yes, both wants the keyboard, but they want it in different manner. You can configure them to work together without too much problems. All is about configuration and the learning curve.
Main issues I've faced are: managing parentheses and brackets (just choose which one is going to do this), templates (not a real problem: use tab for one and space for the other), suggestions (configure different keys for each tool).
CodeRush plugins and Resharper plugins works well together and the result is a true delight. There are no conflicts between the tools. Just take two weeks to use it with easy.