The advantage of client certs over U2F is that client certs use the same proven mechanism your browser uses to verify the server's cert, and can even be handled

The advantage of client certs over U2F is that client certs use the same proven mechanism your browser uses to verify the server's cert, and can even be handled by the web server. It's also seamless for the user - if needed you can be logged in right from the first request. U2F needs to be implemented over the top in the app itself and the login process is at the minimum two steps (no way to login from the first request).