We are running synchronized Web Crossing servers (distributed servers/master-slave/source-mirror). Are the databases identical on the machines? In other words, is it sufficient to back one of them up, or do we need to back them both up?

Yes, the database is identical on all machines.

You may perform a manual backup on any node in the cluster via the backup control panel at any time.

However automatic (scheduled) backups occur only on the master for performance reasons.