I personally prefer CodeRush.
I find R#'s interface drives my (admittedly minor) OCD tendencies crazy. The little lightbulb insists on appearing on the far left of the screen, even if it's advice pertains to something in the middle or on the right. I find it garish and distracting.
By contrast, CodeRush's equivalent smart tag is lower contrast and smaller. It is therefore capable of locating itself within the code without distracting from said code. I find I can ignore this SmartTag when I need to, and it is always right in front of me when I decided I need it.
It is mainly this, that has prevented me from wanting to explore R# any further.
As far as CodeRush's feature set: Code Analysis, Refactorings, CodeProviders, Templates, TabToNextReference, QuickNavigation and many more.
I especially like CodeRush's extensibility which has allowed myself and several others to create many plugins for use within it. (http://code.google.com/p/dxcorecommunityplugins/)
CodeRush also has some top quality support and a very active community of users.
Certainly neither R# or CodeRush will suit all users. Every one has their own preferences. However, if you've not tried both, you should certainly do so.
If you come from the R# side of the equation and are looking to test out CodeRush, then you may find the compatibility plugin useful (http://code.google.com/p/dxcorecommunityplugins/wiki/CR_ReSharperCompatibility)
In addition CodeRush has a Free edition 'CodeRush Xpress' which Microsoft commissioned DevExpress to create, and which they have licensed on behalf of every user of Visual Studio 2008. This partnership will continue into VS2010 upon it's release.
If you have any questions regarding CodeRush you can find details for contacting me at the bottom of my community wiki page.
I should say that I do not work for DevExpress. I am what you might call a DevExpress MVP. To maintain this position, I answer questions in the DevExpress forums (and nothing else).
Everything I say is my own honest opinion.
If you have any questions, feel free to contact me :)