Firefox primarily on the desktop, Chrome sparingly. Only thing I like about Chrome over Firefox is the default "sync" method for bookmarks and stuff. Firefox's implementation is annoying and a hassle to set up, while the one Chrome uses has worked without issue.
Firefox's implementation always messes around by organization of bookmarks. Basically, any time I went to sort my bookmarks, they'd reset to how it was before. Plus, the setup of having to have access to two machines (so you can copy the code from the first to the one you're setting up) really makes it a pain if I'm visiting a relative and give myself a login on their computer. Can't access an already-set-up computer? You're SOL.
With Chrome it's just a matter of signing into my Google account.
However, that's the only issue I've had with Firefox. Everything else I much prefer over Chrome, Opera, IE, Safari, or whatever else there is available.