The ADD Health Study asked teenagers the following: "How much do you feel that you want to leave home?" Answers ranged from "not at all" (1) to "very much" (5). Here are means listed by religion:
Mean "want to leave home" score (N = 6,361)
Assemblies of God 2.34
Jehovah's Witnesses 2.25
Disciples of Christ 2.24
United Church of Christ 2.24
All teens 2.22
Eastern Orthodox 1.95
There is a lot there, but let me mention two items. First, I looked into this question because I suspected that Muslim kids were less happy at home than other kids, and the data back me up here. The gap between Muslims and kids from the AME church (a black church) is two-thirds of a standard deviation--a large difference. (I'm a bit surprised that blacks teens like home so much).
Second, teens with no religion rank third on the wanting-to-leave-home scale. You might expect them to be happier since teens want more freedom, and religion can feel like more restriction on top of ordinary parental restrictions. But there it is.