Sorry, Op you do have to go and look and make your own mind up. You can't do it sight unseen.
I also have one state and one private
Advantages of private
More sport, if that matters to you, my dc aren't sporty so it's a red herring
Better music, again if that's important.
It's a selective prep, the kids there are pretty clever and that creates a very sparky enivornment, lots of ideas being bounced around
Mainly fantastic teaching (though the state has a lot of brilliant teachers too dealing with a far more challenging bunch). The teaching is to a higher level because of the intake though that doesn't really seem an issue at primary level, I know so many super-bright, super-interested-in-the-world children at state schools who are clearly doing brilliantly.
Better feedback - though I think the state would give better feedback if there were problems, because dc were doing well I just heard "oh, they're brilliant." In fact dd1 isn't brilliant at many things and the private school focuses on this (as well as encouraging her in the areas where she's strong)
Feeds into a fantastic secondary - the main reason for the choice
Advantages of state:
Saving on fees
Cheaper and less silly uniform
More school trips and genera "fun", partly because terms are so much longer
I think better pastoral care, more emphasis on the "whole" child, partly as a result of children coming from wildly varying backgrounds and the school trying to celebrate something about everyone - not just the high fliers. This is not the case at the private school
Most importantly to me - the social mix. The private school is very limited. We're in London and most parents (not us) work in the City. The state primary has children of every imaginable background. London has become so divided socially that it's become increasingly important to me that my children mix with children who don't live in huge houses and go skiing in February as a matter of course.
All in all, I advise people to go state and move private only if they're not happy after a year or two.