As far as I can tell, wire is fine regarding privacy. All chat content and metadata is end-to-end encrypted. I am not aware of any additional, unnecessary data collection. You can check their privacy policy at https://start.wire.com/privacy-policy
The main reason for concern comes from the wierd, intransparent move of their holdings company to the US in 2019 (see https://techcrunch.com/2019/11/13/messaging-app-wire-confirms-8-2m-raise-responds-to-privacy-concerns-after-moving-holding-company-to-the-us/ for details)
In 2020 the holdings company moved back to europe and is now located in Germany.
For a comparison with other messengers see https://www.messenger-matrix.de/messenger-matrix-en.html