I also like the fact that Wire doesn't need a phone number (unlike Telegram, Signal, WhatsApp and similar applications). You can sign up with an email address and use it. Of course, Wire is end-to-end encrypted, syncs across devices (unlike Signal) and has native^ multi-platform/multi-OS support where each device is independent and doesn't need the phone to be around (unlike Signal or WhatsApp).
On the topic of open sourcing the server, it's a good move from the security audit point of view. But until any of these new age apps/platforms support federation and decentralized communication, there's not much use for the masses to look for servers run by specific people.
^: As mentioned in a comment below, it's an Electron app, but I meant to indicate that there's an app that you can install for each platform without having more prerequisites (unlike Signal that requires Chrome/Chromium to be installed first).
[1]: https://wire.com