A.D.
if you are concerned about your daughter's education and have the money to spend, i would honestly look into some sort of home school program, and that doesn't mean you have to do the schooling. i know a woman who does homeschooling for kids who do not flourish in a public school system, and she is amazing. she takes these kids that are 1 or 2 grade levels behind where they "should" be, and puts them a grade level or two ahead of their peers. if you can find something like that, it might be far more valuable than public vs private.
i have a friend who is 26, and she was VERY self-motivated to get the most out of her education. so even though she went to one of oregon's poorer, lower rated school districts and her parents were not as involved in her education as they could have been, she is now on the fast track to get through law school (3 years as opposed to 4 or more) after working her tail off to graduate from OSU with a 5 year bachelors in 4 years. another friend of mine went to a private school her whole life, and her parents would have been better saving the money and sending her to public school. she is 30, got kicked out of her high school and never went back to school (though eventually got her GED within the last 5 years), never went to college, relied on everyone else to drive her places until she finally got her driver's license 2 years ago, has only ever worked mcdonald's despite being a single parent and needing health insurance for her 2 kids, and has no interest in doing better for herself or her kids. based on that, i would say it's not the school that makes the education. it's the teachers and the parents who stand behind the child and give the child the tools to learn and can hopefully instill a love of learning in the child. but ultimately, the decision to make use of a good education falls on the child.
good luck with your decision.