Depends on what features you need. I don’t need unlimited storage. Dropbox’ sync is far more reliable (see my other comment). Dropbox has Paper, which supports LaTeX equations and can be exported as Markdown. Dropbox has great integration with Microsoft Office and Office Online. Dropbox supports file requests.

The only relevant feature for me that Google Apps offers over Dropbox is email. But I highly prefer FastMail, which respects standards (IMAP, CaldDAV, CardDAV) and not Googles broken implementations.

Sure, but if you literally just want somewhere to store files, then Dropbox is cheaper. That's one reason why someone might prefer it.