My understanding is from reading another thread there are certain apps that have disabled the use of Face ID especially certain banking app so I'm not so sure if that is 100% true.
The Amazon app also supports Touch ID and allowed me to log into my orders using it on my iPhone 7 Plus. On my iPhone X Face ID doesn’t work as the alternative way and I have to log in the old fashioned way using user name and password.
You don't get to choose between FaceID or Touch ID. The operating system seems them as one, so depending on whether you use iPhone 5S - iPhone 8/8+ or iPhone X, the operating system uses TouchID or FaceID. The apps don't specifically ask for TouchID or FaceID, they just ask for biometric authentication and the operating system uses whatever underlying biometric hardware that is available and sends the result of the authentication back to the app.
If what you're saying is true, then it seems like those apps are simply disabling biometric authentication on the X, as they can't choose to disable FaceID and enable TouchID, they have to completely disable biometric authentication if they detect the app is running on the X.