Never heard of Matrix before (as a protocol) what's it's advantage over XMPP?
https://news.ycombinator.com/item?id=10040302
Lots of discussion here.
The conceptual the prinicple difference is that XMPP originally is about sending messages while Matrix conceptually is about 'syncing state' (like a mini-graph database).
It's heavier and leaks metadata.
The only one that sprouts to mind is it is currently more popular and has fancier mobile clients. Besides that, it's slower and more resource intensive.