They are essentially the same thing. database_xml_deadlock_report was introduced to provide a method for retrieving deadlocks for Azure SQL Databases by scoping the deadlock event to the victim database and allowing users to create database scoped extended events sessions.
See this link for more information. Basically, the XML Report event field should return the same information and that is where the important data is. The other three fields (database_name, server_name and deadlock_cycle_id) are obtainable from within the XML report or from the global fields.
You can basically use either one.