Retro

Having worked in the public sector and now in the catholic private school sector, one biggest noticeable difference is the moral teaching given through religion studies.  Things I find more important over academics as a human being.  Moral teachings such as what's right from wrong, consideration, remorse, respect.  (Most students in my school are not catholic, FYI) In the private sector there are more extra curricular activities - eg. out-sourced tennis instructor starting from grade 4 level, young writers club, leadership groups, etc.  (I personally did not get to learn tennis until grade 10, studying in the public system)

For highschool, if your child is extremely brilliant and talented and have the potential to go to a high caliber university, I personally would recommend going through the private sector as well.  Those universities look for a lot more than academics - extra-curricular activities (eg. debating club, volunteering groups, chamber choir, orchestra/band, school reps, etc) are also essential.  Public schools may not be as well endowed in providing these opportunities.  

Having said that I went through the public system all my life and I'd like to think that I turned out quite alright.   

That's my 2 cents! Goodluck!