My parents sent me to state school. They cared about my education.
DH's parents sent him to state school and they cared about his education.
We are planning to send our DTS to state school and we care about their education.
DH and I went to university with privately educated people, we work with privately educated people and we have surpassed many of those same people in terms of career progression and pay.
My boss sent his daughter to private school. There were seven in her class. She failed her GCSE Maths and got a D in English. Two of DH's cousins went to private school and failed their GCSE and this was a supposedly top school!
The biggest problem with too many state schools imho, is the social attitude towards education. If you have an area where too many people do not value education, that will impact on the schools. In that respect, you cannot blame people for wanting to avoid those schools by moving to another area or by going private. However, I went to one such school and it is interesting to note that children of immigrants tended to do better than those with indigneous parents. Why? Our parents thought that the free education provided was excellent and they encouraged their children to make the most of it.
In my experience and imvho, what really matters is the home environment, whether you send them to private or state school.