I think you really have to look at both options that you have. My kids did preschool in a private one, mainly because they did not qualify for the public preschool, but also I liked them getting Bible as part of the curriculum.
Other things to consider: Cost, staff - child ratios, curriculum, hours (what is more convienient for you, if one is full day, do you feel your child is ready for that) If a lot of thier friends are going, they might be more comfortable where they are.
No matter where they go, I suggest getting very involved in the school. Volunteer and be there. Communicate with the teacher regularly, be part of a team with her. (or him)