This very much depends on implementation and the data stored. For instance if the passport has a chip with your DNA information then it is relatively secure since it is really something someone else cannot fake, well they can if you reference Gataca, so it would not matter if the db was hacked or not assuming the implementation is by physically taking a DNA sample. As others have mentioned fingerprints and facial scans can be duplicated but mostly because they can be digitized and analyzed easily, DNA samples cannot without very expensive machinery. In other words, at this point in time no one will use a blood sample to access your bank account online, if they did then it would be more susceptible, however I can see governments using DNA analyses to verify the identity on a passport.
The problem with a lot of common bio-metrics is that there are fairly easy ways to fake it, like rubber finger prints or makeup which can be faked without ever physically accessing the person, taking blood or skin samples requires access to the source of the material and is harder to trick people with.
Of course the alternative is a password or a signature which can have it's own issues, I would say if there was a choice fingerprints would be more secure, if for nothing else it would be a lot more trouble for someone to obtain then a password.
Hope that helps