XMPP by its extensible nature can be a social network (Movim), a community organizer (Libervia), or can be used for basic presence, etc. & these can sit atop your XMPP server (Prosody, ejabberd, etc.). Matrix, without extensibility, is kinda relegated to chat (text, voice, video) only. The push-based servers make clients efficient, and both Prosody & ejabberd can be UnifiedPush server with a basically a boolean flip in the config—interestingly can be a push server for Element & other Matrix clients instead of relying on Google.