I'm not familiar with Zimbra.
RSync is an excellent tool for what it's designed to do: to keep a remote system sync'ed to a master system. It can be put to work for a Backup solution, but I would only use it as part of a solution.
There are a wide range of solutions for backup, depending on your specific needs. (And, as pointed out, a mail system backup may have specific needs other than to restore the entire system to a previous state - including all the unread emails, since deleted by the users.)