Matrix is like chatting via GIT (distributed databases) and tends to be a team messenger like Mattermost or Zulip - XMPP is structurally like email (but with options like online status, currently typing, last online, ...) and is often used by large messenger services (e.g. WhatsApp uses its own variant of XMPP).

XMPP is the only system that can and may(!) be used wherever email is in use.

XMPP is just as "modern" as Matrix, but has a _different _ data storage/distribution idea.

Comparison: https://www.freie-messenger.de/en/systemvergleich/xmpp-matri...