personally in my opinion it doesnt matter if its "private" or "public" its not going to change if your child wants to learn! nowhere does it say if you go to a private school you are going to be "smarter" or have more job opportunities.
i personally attended a private all girls school where the fees were thru the roof i can tell you now most private schools have a "registration fee" which is around the $100 mark just to sit there and fill out forms mind you with paying that $100 that does not garentee you will get accepted into the school.
then at the school i went to if you got accepted, you had to pay a acceptance fee of $800

then it was tuition fees of 3,640 per term.... times that by 4 then by the 12 years i was there and well you get the picture.
admittidly i am now a couple of months off a degree in nutrition but i worked my ass off the last 2yrs i believe it is up to how hard your child trys.
you could pay all the fees work your ass off only to find your child has NO interest in school.
if you can afford the private school lifestyle then go for it! i know lots of people who have attended public schools and they are just as well education if not more!
public schools offer assistance in trainee ships/apprenticships etc
the only difference is the the classes are smaller in a private school which means more one on one time with the teacher!

hope this helps and hope i didnt offend anyone. (this is my opinion only)