However instead of worrying about entering your password on the wrong site, you have to watch out for accidentally pairing and creating an account on a site you didn't mean to and then inputting information into it thinking it was some other site. This leaks the information and what your host was but is somewhat better than the case of entering your password as they can't use what they have been given to impersonate you.
Clearly more secure than password based authentication. I hope it will finally kill phishing attacks.
My argument is based on the increased entropy of cryptographic keys replacing user-chosen passwords. So brute-forcing and social engineering becomes harder.