I was lucky enough to go to a very well known public school and I have always been privately educated. however my DH was not and he happened to be at one of the top comprehensives in the country (and a very good state primary) with a better reputation than many of the top public schools.
I think that it really depends on where you live.
However DS always says that he was never pushed as much as he could have been at school and had quite laid back parents. I on the otherhand was really pushed. DS is quite lazy and I am not (he agrees with me). he is much brighter than I am.
I think that it really depends on
a) where you live - why pay for the education if you donlt have to and you can get your child into a good primary school
b) what your plans are for the secondary education. If you are being "primed" for the public schools then you do need to make sure that the primary school you choose is able to get your child in.
c The child - especially for secondary eductaion. there is a big difference emotionally between the academic pressures of some schools v a nice private school. I was a boarder and I know some people hated it while I really enjoyed it. Also some children do ot thrive until they leave and I have not actually done that well in my career (I've done OK) but there are people who did not do as well as I did at school who are now captains of industry and top in their fields.
For MY DS I think I will privately educate for primary as I feel that it is actually more important to get a really good grounding and believe in educationf rom an early age. Jury's still out for secondary - although sswaying for private. We live in London so the choice is pretty shit for state.