Private school is not better because essentially it all depends on how much you are willing to work. Although, private schools may make work a little easier, it all depends on your work ethic. If you go to a private school and don't work, then you're not going to get a good grade. The only advantage of private schools is the working environment outside of you, but that's all. To conclude, I believe that anyone can get the grades they want to achieve in a regular school, without the need of a private school.
I agree with you to some degree. Working in a private school boosts your confidence and there are teachers willing to help you work. You cannot necessarily learn everything yourself: you need the guidance of teachers, and not any teachers, teacher that are willing to help you and make sure you understand. Most of these kind of teachers are found in private schools or schools where children come to learn. ( private schools)