If the public schools will work with you and not be inflexible, I really like working with them. For one, the money saved can go into enrichment opportunities outside of school (book budget, camps, etc.) without as much debate. Secondly, while it may not be true at your private school, many are really struggling financially and have more limited resources than public schools (more outdated computers, lower salaries for teachers/less qualified, etc.) Small numbers and controlled setting, less bureaucracy are clear benefits of private schools.
Another benefit of public schools, at least here, is that they are an education unto themselves by teaching kids about diversity, how to handle situations (sometimes unsavory), more "real world". As parents, we think we'd like to shelter our kids from some real world stuff, but it's really beneficial to have them understand how to handle it too. My DS's HS is a title 1 school (70% free/reduced lunch, large population ESL, illegal immigrants, pregnant teens, gang-bangers). This has been very eye-opening for him. The principal told me that they have honors kids go to ivies precisely because they're from a school like that and have learned more about life.
