It does depend on the school. But DH and I would much prefer public so our DD is going public next year. I attended private (catholic) most of my schooling but did around 3 years of public, and I liked public so much better.

Pros of public -
*low fees - the extra money can be put into extra cirricular stuff, tutoring, etc.
*secular education where you can opt out of scripture (this is important to us as I'm athiest and don't like how catholic schools sell catholicism as truth rather than a possibility)
*tend to be less elitist

Cons:
*sometimes have less resources. An expensive private school I went to in high school had the best of everything. They were charging ten grand a year (this was 15 years ago) plus attracting quite a bit of govt funding. They had brand new buildings, a huge hall, while the local public high was falling apart.
*sometimes have larger class sizes