Obviously different children have different needs and some schools are better at catering for one particular type of child over another. You have to look at your own children and assess their own needs.
My children probably would have loved more formal learning straight away and less learning through play, as that would have suited the way they like to learn a bit better, but learning through play hasn't killed them or irreperably stunted their intellectual development and it has helped them become better socialisers and team workers. They are, in any event, bright enough that they only need to be taught a concept once to understand and apply it and frankly by half a term into reception would have found it rather boring to be asked to do numerous simple addition sums on paper, because simple addition is not exactly difficult. I wouldn't, therefore, be looking to formal learning as an automatically better system, I would be looking to see whether the school could differentiate sufficiently for my children so that they didn't get bored or separated permanently from their peers to work with older children, something which my dss' state primary appeared to be reasonably capable of doing (and at least with learning through play, if the academic learning bit is a bit beneath you, at least you still get to play!...).
Basically, I know my children will be at least 2 years above the average by the end of year 6 without having had to pay for school fees - not because their school churns lots of children out like this, because it isn't that middle class, but because my children are who they are. Maybe if they went to a highly academic private school, they would end up 4 years above the average, but I'm not sure that's worth the sacrifices we'd have to make to send both of them to private prep schools, or possibly the sacrifices in free time they would have to make. And in many private schools they might come out the other end no better off academically, or possibly worse off academically and in other ways, because not all private schools are particularly good, whereas my dss' primary school is, in my opinion, lovely! I'd love the class sizes to be smaller, of course, but at least they've got lots of potential friends to choose from, live in the community where they go to school, have committed teachers and a well thought out and stimulating curriculum. Oh, and a very clear understanding of how lucky they are.