I'm glad I went to a private school because it offered me a fantastic musical education (one year's free tuition on an instrument of my choice in year 7, orchestras/ensembles/choirs, myriad concerts, etc.), which I don't think most public schools have.
It wasn't a hyper-competitive place like I'd imagine MHS or Mac.Rob would be, but there was enough of it to keep me on my toes. My school wasn't "elite" academically but we'd have at least one 99.90 or 99.95 each year.
We had some excellent teachers, which some public schools unfortunately just can't afford, e.g. my English teachers all had law degrees (overkill much?)
I don't think I would have done as well at a public school because I just lack that self-motivation, so in my case, yes a private school was instrumental in helping me to succeed.