I use Safari because in my experience Chrome is rather buggy on a Mac. Particularly with regard to Spaces. E.g., if I move a Chrome window to a different Space, all of my other Chrome windows will tag along for the ride. It makes using Chrome rather unbearable. Additionally, Safari's interface for managing bookmarks is much nicer.
I use Chrome on a Mac with a half dozen spaces with multiple monitors and have never had problem moving between spaces. Out of curiosity are you using the release, beta or dev channel?
I just use the standard release of Chrome. I Googled about the problem several times and all I could find out is that some people experience this issue and others don't, and no cure was known. The problem did not go away via numerous upgrades of Chrome, so I eventually gave up.
