Personally, I don't think it matters what school you go to and whilst grades perhaps have some kind of correlation with the type of school, it's obviously still down to the individual.
People that want to succeed and work hard will do so wherever they are. You get grammar school kids that don't appreciate the chances they get and still muck up their studies while there are comprehensive students that work their butt off and end up with amazing results. With GCSEs getting erm 'easier' and the millions of past papers and entire textbooks for sale at bookstores and online, it's really up to the individual. Yes, with different schools comes different opportunities but really, if you didn't take the initiative in the first place to realise how important grades are and WORK, then maybe you wouldn't suit ANYWHERE.
I go to a top grammar school where the pass rate at GCSE and A level at 100% and there are still some PRETTY BAD teachers around. And as for support, you don't really get any...apart from the odd few cumpolsory classes for borderline students near study leave time, teachers rarely take such a personal interest in your work. For those subjects, I just had to self- teach myself.