I think it really depends on the quality of your public schools. My kids all go to public schools (4th grade, Young 5's, and 4 year old preschool) and I am very happy with it. We have very good schools in our city and I like that they go to school with a relatively diverse group of kids. (Different races, income levels, backgrounds, etc.)
If the quality of our schools declined (a real possiblity with continually decreasing funding) I would have no problem putting my kids in the local Catholic school (our only private school option) but for now I am satisfied with the public schools.
The one disadvantage I find is that along with the diversity in the schools comes exposure to things that I might prefer they are not exposed to but that is going to happen sooner or later regardless. And I try to look at it as a teaching opportunity as it comes up.

I would put my child in the district that they will go to kindergarten to. Lots of times the preschool will follow the same curriculum as the district.

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)

My sis and I both switched to public K when we could. It was attached to the elementary school where we would go so we had a chance to get acclimated to the environment, teachers, etc. while on a smaller scale. I think it made first grade less of an adjustment for us to make.