well no one can tell you
you cant do a controilled experiment
it just depends on school and kid
and extraneous unfathomable combination of circumstance
i have two girls dd1 went to indepoendent school dd2 16 months younger went to state comp
dd1 has been to uni been abroad confident socially aware just got her first graduate job for high powered polotical lobbyist co and has great bf etc etc
dd2 did disnamlly at school, lacks confidence, had terrible teen probs left school went to coollege dropped out and went back to school had a baby worked in pub and as a cleaner full time bf is a total loser
but she has recently picked up in confidence she does have ambitions she is clever tho doesnbt have the exams to show and has just been given a permanent office job she likes and is thinking of doing something in accountancy
she and i both think if she had gone to dd1 school things would have worked out differently
but maybe nbot