BIG DIFFERENCE, public school is public school. Almost all children of the U.S. go to it. It is government run. You have to go. A church is private and people choose to go to it.
EDIT: So you are advocating rebellion for children not to listen to parents? THEY ARE KIDS. They are raised according to the parents up till the age of 18. They can then decide what they want to do for themselves--whatever it may be. Go to church, or go fuck each other on the side of the road...Their choice.