Cloud storage platforms like Dropbox and Google Drive have some genuine advantages over USB flash drives: You obviously don't have to remember to bring your flash drive with you in order to access your files, and the risk of losing your files is relatively small compared to flash drives that can break, malfunction, be misplaced or get stolen. On the other hand, cloud storage also has its drawbacks. For many of us the issue of security is a deal breaker. Just today it would appear that Dropbox user accounts have once again been hacked. Even if you go in a change your password right away, in reality it may be too late. You won't know if hackers have accessed your private files until unknown charges appear on your bank statement, private pictures are posted online, etc.
One solution is to keep your sensitive files off of cloud storage and on a flash drive instead. If you tend to leave your flash drive at home, you might want to consider a flash drive that attaches to your key chain. Encrypting your flash drive with TrueCrypt or BitLocker adds an additional layer of security.
So the question of whether cloud storage or flash drives are better is really a false dichotomy. Both are useful tools that must be used correctly and for the right purpose.