Hi G.,
I taught public high school but my son goes to private school. My husband and I were both educated publicly and had great experiences.
My opinion--there are wonderful teachers in both public and private schools. Involved parents (involved in the school AND in their children's lives) are the key to success in school--no matter which school it is. ALL schools have problems and pros and cons.
Just because a school is private does not necessarily mean that it is not affected by the economy (unless of course, you're talking about a private school that costs $15K a year, but even those fundraise).
If you want a school where your child will receive a specific religious education or will have a specific focus of a spiritual or ethical nature, then perhaps private is for you. Yes, class sizes are usually smaller, and in my opinion as a public school teacher, smaller class sizes are better--fewer chances for kids to get "lost."
We send my son to private school because of the spiritual focus, the smaller class size, the community environment, and the fact that the parents seem to be "like us".
Public school has more diversity and may have more class types offered (AP classes or electives, for example, or even sports and clubs). More kids means more of a selection of possible friends for your child, too. In general, more is tolerated in public school--religious beliefs, behavior, special needs, cultural differences. More teachers and coaches can mean more role models, too. Public school can be less intimidating too (I have a friend who took her son out of a private school because it was too structured and accelerated--her son developed major anxiety).
I do not think you can mess this up as a parent, as long as you are involved and pay attention to the type of child that you are blessed to have--is your child introverted or extroverted? Independent? Very social? (Think about colleges--a small liberal arts college may be great for one kid, while a large, science-based university may be perfect for another).
Good luck!
:-) D.