Did you watch the keynote? They said that your phone could mistake 1 fingerprint out of 50,000 fingerprints for yours. Doesn't matter if that 1 fingerprint IS not identical to yours. The technology isn't a fingerprint expert (a person) looking at the lines. It can make that mistake 1 in 50,000 times. BUT with the face, it's 1 in 1,000,000 times. So while a person might mistake your cousin (who looks like you) for you, the technology won't.
So, this technology (in theory) is LESS likely to mistake another's face for yours than the fingerprint software is to mistake another's fingerprint for yours.
Don't confuse the technology/software with a person. It is NOT a person. That fingerprint button does it's best to get all of your print--sides, tops, etc. But it can make mistakes (my first phone with the button kept failing to recognize mine--the one I have now, 6S, does fine). A fingerprint is small. BUT a face is bigger and the software here, from what I'm understanding, can map more than that fingerprint button. If that's the case, then it has more information to work with and is more likely to recognize your face than the fingerprint button is your fingerprint. So. Uniqueness of fingerprints isn't the point. It's what the technology can map. Facial recognition can map more = more accurate.