Backing up Master-Master replicated MySQL databases
This is a Master/Master setup, so I would advise the following


Do not mysqldump from either Master. Both Masters should be used as Active/Passive


Active : Receives all writes
Passive : Replicates from Active (Hot Standby for Failover)

Add an additional slave from each Master


Can be low commodity in CPU since SQL thread processes one command at a time
Should have the same RAM and plenty of Diskspace for Backups



If you do go with additional slaves, you can use either mysqldump or xtrabackup.