It might depend on the platform.
Assuming you're talking about a smartphone app, I'd leverage off the built in security features of the platform where possible and use a password as your backup.
On iPhone 5s, and all of the iPhone 6 variants I'd leverage off the built-in Touch ID technology and use a 'fingerprint login'. This is actually a lot faster, more secure, and provides an overall better user experience. That's why many password and banking apps now provide the option for iOS users, with a password as a backup.
I'd also leverage off the similar technology found in the higher end Android market. This may be a little more challenging because of the fragmented nature of the Android hardware industry, but is certainly worth the effort.
And there's no reason why you couldn't offer it for your iOS users first before rolling it out on the Android versions of the app. In fact that's what many of the banks have done, with their Android versions still using a password login while the iOS versions offer a choice of either.
If you're talking purely about a website app, then I'd offer the option of both Facebook and Google logins, as well as a registered user login.