Using this very good comparison site in German as base and ignoring the similarities:

Technical

• XMPP allows for various different client styles while Matrix doesn’t
• Fully featured, mature text-only clients for XMPP exist, but for Matrix there are only beta text clients available
• Matrix handles/addresses are always public in chat rooms while XMPP chat rooms can be configured to hide them
• Matrix has multi-server chatrooms for reliability in case of server or network issues while XMPP chatrooms alre always bound to one single server
• Matrix Chatrooms can be encrypted. XMPP chatrooms can be encrypted or not encrypted. (there’s no further explanation on this point, I assume it’s meant that Matrix servers can turn on encryption and that’s it, while XMPP servers allow the chatroom administrator to decice and do not force one or another)
• Administrative data is stored on one XMPP server. Matrix administrative data is stored on the servers of all connected users
• XMPP is modular and the protocol itself can be extended while Matrix is monolithic
• XMPP protocol uses XML while Matrix protocol uses JSON
• Matrix focuses on reliability and availability of chatrooms, XMPP focuses on features and extensibility
• XMPP uses less system resources than Matrix
• Chatroom data storage is done only on the XMPP server the chatroom is running on, while Matrix stores chatroom data on all of the servers of the connected users
• XMPP directly sends a message if the connection is open, otherwise a push notification is sent. Matrix only sends a push notification to the client and the client has to pull the message from the server

Organizational

• XMPP is an IETF standard while Matrix isn’t
• XMPP board and council are equally elected by all members. Matrix is a “single-party system” where the board decides who is allowed in the board.
• For XMPP all members are allowed to question/check/validate the board and council and there are annual elections. For Matrix, the Matrix.org Foundation and New Vector ltd. expect rust from the community.
• On the XMPP board and council, all actors have to name their interests and their employer (this is to prevent having more than 15% of board/council members from the same company which would give a single company too much power). For Matrix there is no known information about such a clause.