Whether fingerprits or iris patters, it would bring down security so long as it is operated together with a fallback password.
Threats that can be thwarted by biometric products operated together with backup passwords (rescue/fallback/ alternative passwords) can be thwarted more securely by a password-only authentication.
We could be certain that biometrics would help for security ONLY WHEN it is operated together with another factor by AND/Conjunction (we need to go through both of the two), NOT WHEN operated with another factor by OR/Disjunction (we need only to go through either one of the two) as in the cases of Touch ID and many other biometric products on the market that require a backup/fallback password, which only increase the convenience while bringing down the security.
Incidentally, it is not possible to compare the strength of biometrics operated on its own with that of a password operated on its own. There are no objective data about the overall vulnerability of biometric solutions (not just false acceptance rate when false rejection is near-zero but also the risk of forgery of body features and the risk of use when the user is unconscious) and that of the passwords (not only that it may be as low as 10 bits or as high as 100 bits but also that it could be stolen and leaked.)
Such a terrible nonsense as the “password-dependent password-killer” should be killed dead lest the good reputation of biometrics as excellent identification tools for physical security should be damaged. Biometric solutions in cyber space could be recommended to the people who want better convenience, not to the people who need better security so long as they are dependent on the backup/fallback passwords.