Kerberos' use of symmetric keys is actually one of its strengths. In a post-quantum world, kerberos is significant more resistant to attack.

Kerberos suffers in other areas, suck as only doing authentication but not authorization, and realm discovery is not trivial.

EDIT: Thinking further, I think you are taking about the fact that you need to get a secret key (keytab) from the KDC to do authentication, where as in other auth technologies you are giving the public key to a server and no sensitive information ever has to be transported. That is true.