Amazon is a public company. You can figure out what AWS is valued at by the market, by doing some math, and reading some annual reports. Admittedly, the web store portion of Amazon clouds that value, no pun intended...but you could probably take a look at Amazon a few years ago, before AWS became a major contributor to their bottom line, to make sense of the numbers.

AMZN currently has a market cap of $95 billion. It's safe to say AWS is worth significantly more to the market than Dropbox; as it should be.