Never heard of Matrix before (as a protocol) what's it's advantage over XMPP?
It's heavier and leaks metadata.
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).
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.