Dropbox doesn't use S3 anymore. They did initially. That being said S3 is a pretty good solution.
What do they use now?
Possibly OpenStack's Swift. Its API-compliantish with S3.
Just because Dropbox uses S3 right now doesn't mean they always will. If S3 goes down, Dropbox will probably just use something else.
Honestly curious...what's your knowledge of the company named Amazon? That is, how much smaller do you think Amazon is (by any metric, market cap, revenue, size of engineering operations) compared to Dropbox?