I have bursary/scholarship kids (a mix) here too.
We had so many agonising discussions about this, and many years down the line are still not sure whether we have/have not done the right things but here are some points to consider.
We are a working class family, which means working both long hours and have no family connections, friend connections in the business, medical world etc...our education level is good but we don't have the advantage of being able to have a parent at home to nurture additional learning, etc...so this is another disadvantage for people like us.
Private schooling enabled our children to mix in an environment very different to their immediate family and friends, as well as offer extracurricular and other opportunities as part of their school day.
It also meant much stricter/pushy teachers/standards which we would not have been able to enforce at home.
Our children were transformed going from good state primary to private, but then I know many middle class families with connections, money and plenty of time who have the same going to standard state schools. Of course for them it doesn't make that much of a difference.
As for the thirst for learning, I don't think you can buy that or nurture it really. I think that is down to x factors that can be found in either sector and also include the child just being that way inclined. I didn't mind the spoon feeding received at school as in the state sector I found much drilling and spoon feeding was being done at home by the resident parents and/or tutors, so not much difference there.
Of course some children will be naturally brilliant, self motivated and super bright, but most children in reality will be just average or just below and above, and this is where input either at school or at home can make a huge difference.