The single biggest difference is that Matrix is effectively a realtime decentralised conversation store (like NNTP or a decentralised form of IMAP), where conve

The single biggest difference is that Matrix is effectively a realtime decentralised conversation store (like NNTP or a decentralised form of IMAP), where conversation history is replicated equally over all the servers participating in a room - a bit like Git. Each partcipating server owns the conversation equally; none is a single point of control. XMPP is a message passing protocol at its core, more like SMTP. MUCs have a single logical focal point of control.