Matrix is more like a state synchronization service than a way to send messages. If I join a room on another Matrix server, my server will begin maintaining a copy of that other sever for me to use how I like. If I shut my server down for a day, it will sync back up when it comes back.

I’m not sure if XMPP works like that, but I always thought it was more like email: send a message, maybe retry a bit, but that’s about it. Not sure how transient things like presence, read receipts, and typing notifications work either, across servers.