I can only tell you our experiences, OP, it is a hard choice for anyone (who has a choice) to choose their child's school - state or private or both one after the other - especially the first time around 
We're in London. We looked at state and private primaries, and chose the school we felt had the best pastoral care, the happiest kids, and the most engaged. It happened to be a state primary. I felt happy that my girls (who are pretty privileged) would have a great social mix to learn and play with, but that's not why we chose it.
It didn't have the top academic stats in the Borough (and it is a top performing Borough, so that doesn't mean all that much - this school had a different intake to the other local primaries). It wasn't shiny, though it's getting shinier by the year. It does have a big playing field and lots of space.
But it was the people who work there who did it for me. The way they worked together, what they modelled to their pupils, the way they knew and cared about the children in their care. And the kids, who ran up to the then Head and the Deputy to tell them what they were doing, and couldn't wait to tell us, visiting strangers, what they were learning.
There is always a bunch of kids who leave at 7-8. Every year. Mostly because their parents are terrified they won't be able to get them into a decent secondary school unless they are prepped at private schools from 8-11. And fair enough, I understand that.
We had to make the decision for dd1, and it would have torn her apart to leave her school - she was so happy, and doing well. She's now in Y5, and is doing so well (we've filled in one small gap with maths confidence by giving her a term's worth of maths tutoring once a week) that I think she stands as good a chance of getting into a good selective indie as her peers who left at the end of Y2. But it did feel like a gamble at the time, admittedly. I know it was right for her, though.
dd2 is in Y2 now, and I think we'll keep her in - though all her best friends are leaving for private schools (siblings there, or parents who teach there) or to go back to Oz or wherever. But the school has grown academically as well as in other ways, since dd1 started there - and what will be will be. I'm not worried.
I suppose...it all depends on a) the child b) the school c) your priorities. Good luck deciding, I honestly don't think there's a right answer!