Matrix uses an encryption protocol of their own devising that employs the double ratchet, which is one component of Signal Protocol. But it's not Signal Protocol, it's their own thing.

Yup, just to reinforce from the Matrix side: Olm is an independent E2E protocol which happens to implement the double ratchet (formerly known as the axolotl ratchet), but it's not Signal Protocol and it's increasingly divergent from Signal, and it's completely independent of Open Whisper Systems. For instance, we're defining different behaviour for group chat ratchets, called Megolm, following our own design at http://matrix.org/speculator/spec/drafts%2Fe2e/client_server....

That said, we've tried to architect it such that we could implement compatibility with Signal if Moxie and OWS were ever open to it. But it looks like we'll need to first prove that Matrix can support a rapidly evolving yet federated ecosystem without compromising UX or privacy :)

And interesting enough, Matrix faces a different problem than Signal: It doesn't have many good clients at all (at least, last I had checked a few months back). I will agree it would be very nice if Matrix was the dominant messaging protocol that everyone needed to speak with their friends. However, that's not feasible until somebody makes an easy-to-use, beautiful Android and iOS client that doesn't require the user to install multiple bridges or wrangle several accounts to chat with their friends.

Vector is now out on both Android[1] and iOS[2], and the web version of Vector has improved significantly.

It doesn't have end to end encryption support yet, but they're working on it.

1: https://play.google.com/store/apps/details?id=im.vector.alph... 2: https://itunes.apple.com/us/app/vector.im/id1083446067

Yup, it's very true that until recently native Matrix clients have been geared up for developers. Hopefully the arrival of FOSS yet polished apps like Vector (https://vector.im) changes that - and meanwhile one can always benefit from Matrix via bridges from existing polished apps (e.g. Slack!)

Vector and recently Tensor are pretty awesome.

I have no experience with iOS anything, but at least the Matrix Console Android client is pretty good for what I use it for. It even supports multiple simultaneous accounts which I really appreciate. I believe the iOS version of it is very similar.