Sign up with Google or user and password

Many websites, not only social media, are providing the method to sign up with Google, FB instead of user and pss.
I used to go with Google but, I'm finding it better to go the old way, which allows to sign in with different browsers, anidetects etc.
Which method is preferred?

For me, I prefer the old way. Sometimes, I don’t have access to that Gmail, so I’d be stuck if I followed the "new way."