Dropbox has the exact same policies and procedures, they just don't have the same technical abilities that Google has. Quoting from their AUP:
"...you must not even try to do any of the following ...:
...
- publish, share, or store materials that constitute child sexually exploitative material (including material which may not be illegal child sexual abuse material but which nonetheless sexually exploits or promotes the sexual exploitation of minors), unlawful pornography, or are otherwise indecent;
- publish, share, or store content that contains or promotes extreme acts of violence or terrorist activity, including terror propaganda;
- advocate bigotry or hatred against any person or group of people based on their race, religion, ethnicity, sex, gender identity, sexual orientation, disability, or impairment;
...
We reserve the right to take appropriate action in response to violations of this policy, which could include removing or disabling access to content, suspending a user’s access to the Services, or terminating an account."
Quoting from their privacy FAQ:
"Examples of Dropbox processing your data in furtherance of its legitimate interests in operating our Services and business include:
...
- Investigating and preventing security issues and abuse of the Dropbox Services or Dropbox users."