Private contact discovery and other metadata protection claims are largely security theatre. SGX is entirely broken and those with physical (and sometimes even remote) access can dump keys at any time.

They pinky swear they always patch and never dump keys when they have the chance though.

It's a security theater not only because someone broke it, but also because you can always just look at which IPs talk to which IPs. Even Tor has issues with preventing traffic analysis, except with Signal you can observe (or trust) a single party (instead of the guard and exit nodes) to get the data.

It's more of a trust thing than something you can technically solve while still having features like real-time calling. Hence Facebook being objectionable despite having encryption.

They're both hosted on USA-based services, they both have proper encryption on the client and apply it also to calls and video calls. There is no significant difference to me in terms of privacy.

Usability is slightly different, yes, and you might also trust Signal more because they do better PR (they say outright that they're from the USA and get money from Facebook, while Wire has devs in Berlin and claims to be a German company, while taking money from USA investors... which imo comes down to the same thing), or you might trust Wire more because they were actually audited at all.