SharedSafe applies client-side encryption. This approach provides true privacy for your files.
Dropbox on the other hand cannot offer this. Because of convenience features like browser access they have to be able to decrypt your data. So when it comes to the privacy of your files, you simply have to trust them.

SharedSafe supports any Provider offering FTP or Email Accounts (with IMAP access). Here is a list of Email Providers SharedSafe has been tested successfully with.

Of course you can use SharedSafe also with your own Internet server. All that is required, is to install and setup your own FTP or IMAP server software.