Neither is my favorite, but I like
Lauren more even if it is dated. I have known multiple
Laurens who are around my age, which is a draw back, but they were/are nice people. The name is comfortable, solid, and down to earth.
Hannah is a very soft name. It is breathy and gentle. I like the name for a character and on other people, but I wouldn't use it myself. If I were going to name a sweet and physically delicate saint, I would call her
Hannah. For a child that was related to me,
Lauren would be a better fit.