Primary schools tend to be fine, I feel it is the Secondary education that makes the biggest impact on your future. I went to the local comprehensive school, and it was rubbish because the kids just misbehaved and the teachers just couldn't control the classes. It was very stressful for me as a teen, because I wanted to learn. I knew family friends who went private and I was jealous of them at the time. Yes, they had a lot of homework but I feel they were better prepared for things. It may not be the normal case, but as a teenager looking from the outside, that's how it looked. This was 10 years ago though.
I think if I had the means I would go for Private, or at least research the best state schools (there must be great ones out there). A worrying number of state schools are becoming business led academies and from what I hear on the ol' Facebook is that the schools are completely changing they way they go about things, and I personally know 3 young teachers in different UK cities who have quit the profession because it is just not about the quality of learning anymore, just cramming in targets. I guess it does depend on area.
TLDR: If you have the means, go for Private, if the reviews of the particular school(s) meet your expectations. The class:teacher ratio in Private is generally going to be more beneficial than state schools where you can have 30+ to a teacher. I hated my state school. Wished I was given the privilege of going private, or to a great state grammar school. Be wary of "academies".