I can't respond for XMPP, but the same question probably goes for Matrix (or any other open comms standard). Reasons you might use Wire over Matrix are probably if you prefer the app's UI/UX to any of the Matrix clients out there, or if you like some of Wire's more unusual features like sketch-sharing, or if you want compulsory E2E crypto, decent group VoIP calling, or a system which does not consider itself beta.

Conversely, the reasons you might use Matrix over Wire is if you want an open standard for the protocol (simple HTTP+JSON), or an ecosystem of different clients, servers, bots & bridges, or Apache licensed impls rather than AGPL, or implementations which were built from the outset as FOSS, or to decentralise history across an open federation of multiple servers rather than be forced to federate via a centralised service, and bridges through to things like IRC, Slack, Gitter etc.

Video calling works splendidly, which is why my wife and I chose Wire.

Back when our boy was just a few months old and my wife's maternity leave came to an end, keeping in touch with video made going back to work a less difficult. She'd call every time she needed some assurance that we were OK, and I could show her we were, in high resolution.

Signal didn't have video calling back then, and Skype is out of the question because I really distrust Microsoft.

As a service, what it's provided is consistency for the group of friends I use it with. We've tried XMPP and Matrix on multiple accounts and had trouble on the server and client side. Wire is out of the box a great option with open source ideologies and some feature we liked that weren't available with XMPP or Riot.

They could have done the same thing with existing protocols, but I do like the way it was done and how well it works for us, and as a consumer of the service it's satisfied areas where XMPP/Matrix felt.. fragile.

Not that XMPP or Matrix are vastly inferior, there's certainly an issue or two we've had with Wire, but just how well it worked for us immediately was largely why we've stuck to it.

XMPP is terribly fragmented and the clients all suck.

I was able to get my grandmother and non-techie friends to use it. What Signal and Wire have over other encrypted chat is user experience. I'm no longer a tin-foil hat crypto nerd only talking to other tinfoil hat crypto-nerds.

I assume it's the same thing as signal is for me: it's the thing with UX good enough to convince some of my friends to use it. They wouldn't use buggy xmpp, tox clients or things without many of the features like ricochet.

I like testing these tools with cryptonerd friends though.