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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.

Matrix is very extensible. You can start sending your own yc.toastal.test.first event type and put any json as value

Like the other commenter said, Matrix is very extensible, as you can just send custom events as you wish. There's also lots of emerging non-IM platforms built on top of Matrix, like collaborative whiteboards, virtual rooms, embeddable comments, etc.

With the new protocol-level performance MSCs coming around the corner, Matrix is becoming ever more appealing for all sorts of applications.

You can run a functional server for multiple people on a very low-power device.

JMP.chat

Speaking as a user of both element generally and Cheogram/JMP.chat.

I still use both.