Unless notes sits on your OS and doesn't require you to boot up your browser and log into Dropbox then, yes they are competing with google docs. I work with an organization that has dropbox set up for around 140 employees and most of them don't use it beyond the desktop integration, why would they?
In my experience, the most common way to share files is by creating sharable links at dropbox.com. In fact I think that might be the ONLY way that I'm aware of.
