For me it's 'stays connected' For some reason Google Drive will disconnect periodically and there is no reconnect option. You have to exit and restart, and then it needs to re-index everything.

Multiple Dropboxs. New feature, but I can run my work and home dropbox at the same time and they sync to different folders.

Sharing is cleaner. When I invite a Dropbox user to a share, the share appears in their drive. With Google drive, they get access to the share web only but it doesn't sync to their drive. The UI to get it to sync to drive isn't clear, so I end up doing a lot of 'support'

I also find the Google Drive .gdoc files bizarre. They aren't actual files, users don't understand you can't copy them out of the drive to back them up, etc.