From my perspective, Dropbox actually facilitates an old, broken way of creating and sharing documents using desktop applications from the 1990s and earlier. Google, by combining drive with docs, allows users to completely escape desktop applications, which to me is really the next generation of computing. To make this more concrete, if a company adopts Google Drive, they can issue employees much cheaper computers (lowering capex) because they don't have to be able to run heavyweight OS and application software like Windows and MacOS. Dropbox isn't even an entrant into that space, and I don't really see how they could compete.
When I look at a company and find out they're using Dropbox, I always think to myself that they probably made that choice either because they've been using it for a long time, or because they didn't want to go to the effort to change their business processes to really embrace network computing. I imagine office workers running Word instead of Chrome, and that bothers me. Either way, I see Dropbox positioned as a stopgap to allow companies to avoid plowing ahead with new work paradigms while still enabling sharing of files without using things like USB keys.
I don't work for either company, never have. But I remain confused about Dropbox's mission. Short of being acquired by someone, I can't see the way forward for them. But, they just raised a ton of cash, so I'm as excited as anyone to see what they try.
EDIT: I want to briefly respond to the argument in this thread that it's a _good_ thing that Dropbox doesn't tie an office suite to sharing files. I simply disagree. I don't see how that is a real concrete negative to anyone unless it's for political reasons ("I don't want Google to be too powerful"). I _do_ however see how it's a problem for the vast majority of office workers who, using Dropbox, have to either keep using desktop applications or (shudder) create documents in something like Google Docs and then reupload them into Dropbox. So, at best Dropbox's independence strikes me as neutral, but for most people it seems clearly negative.