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 (technical council) and New Vector Ltd. (service provider) expect trust 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.