Most Matrix users use the matrix.org Synapse installation. If the people running matrix.org decided to stop working with other homeservers, the result would be much the same as what happened when Google and Facebook became less friendly to other XMPP servers and stopped interoperating with them. This is not an issue with Ring.
Meanwhile we're also working on supporting decentralised accounts in Matrix, so users can pick which set of servers they can use as a homeserver. This then gives the best of both worlds: a simple thinclient protocol that anyone can implement, and knowledge of precisely which servers and devices host your data.
Basically, Ring and Matrix have totally different architectures, and which you use probably depends on what you are optimising for :)