Firstly, full disclosure: I have just finished running through the full trial period for both Resharper and Coderush, and in the end I spent my money on Resharper.
To directly answer your question - yes, in my experience Coderush is much faster than Resharper. Often with Resharper the entire UI will pause for a fraction of second or so while it performs the dynamic compile to test for errors in the code, and you can visibly see the sidebar refresh. Coderush on the hand added very little noticeable performance penalty.
I stuck with Resharper though for two reasons: Firstly the feature set it provides is simply a better fit for my work style. I gave Coderush four weeks to win me other, but its main selling point (the frankly brilliant templating engine) never made up for the lack of functionality that I had learnt to rely on in my four weeks with Resharper. Secondly I noticed that the performance of Resharper dramatically improved with the latest version the slowdown was only really bad on files that were in need of refactoring anyway - files created with Resharper in mind tended to work very well as there were less errors being flagged.
Both tools have generous trial period though and I had no problem installing, uninstalling and flip-flopping between the two of them, so the best thing I can suggest is to try for yourself. For me Coderush is faster and feels more professional, but Resharper has functionality I wasn't willing to give up.