I think all else being equal, private schools are superior to public schools. It's important to consider how I started that sentence: all else being equal. Obviously parental involvement + public school > no parental involvement + private school.
I went to a private lower and middle school then a public high school, then a private college. In my opinion, the teachers and the overall culture in the private schools were more geared towards teaching and learning, and there was greater pressure to succeed, which is supremely important for young, impressionable kids. I believe this got me started on the right foot, which prevented me from being sidetracked in high school when many of my friends did. The most important thing for a school to do for young kids is to totally ingrain in them the importance of educational success.
I think a quality school is the most important at a young age. That said, I don't think a private nursury school, or perhaps even kindergarten, is necessarily worth $9K a year, but I think if you can afford it, especially in Florida, get the kid in a private school at a young age unless there are quality public schools in your area.
$0.02