There's a qualitative difference here, which is that the emailed file will be permanently backed up and synced to all other computers which have your Dropbox installed. When you're on those other N computers, you don't have to go to your inbox to download the file N times, not to mention edits on any one computer will be synced also.
I'm afraid I can't access Dropbox everywhere, in fact most places where I need it and use an iPhone so when moving files around Email is the easiest for me.