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.