Mangomargarita - I was in a very similar position to you.
DD1 was expected to be an only child, and was at a private nursery and automatically stayed on to the pre-prep school. As we could well afford it for one, we never even looked into the standard of our local state schools. She was in yr 1 when DD2 came along, so 6 school years between them. The pre-prep was a lovely school, but the juniors was not very academic, and DD1 outgrew it. She took a 7+ and went to a selective prep school, which gave automatic entry into the senior school.
The intention was for DD2 to follow suit. She went to the same nursery, but we were having some financial issues and it was looking unlikely that we would be able to continue with fees for both DD's. We began to look at the local state schools in time for DD2 to start reception and were pleasantly surprised. It also helped that the nursery teachers felt DD2 was the type of child who would do well wherever she went. There was no question of moving DD1 at this stage as she was in year 5.
So DD2 started reception at our second choice of local state school and is now in yr3, doing brilliantly. She is classed as highly gifted in literacy, and is given plenty of extension work and generally well stretched. Her Maths is also above average.
It became apparant that DD1 was becoming increasingly unhappy at her private school towards the end of yr5. Although she was convinced she was doing her best, and there was never any question of her not being up to standard for the school, the teachers were constantly pushing her to do better. They always felt she should be working nearer the top of the class, rather than the middle. We never did get to the bottom of this, apart from her being badly organised and easily distracted. But the constant pushing from the teachers was damaging her confidence, and after a while we resented paying for the privelege.
We were concerned about moving DD1 from a social point of view, as all her friends were continuing there for yr7. Also, we were well aware that she would be a year or 2 ahead if she went to a state comp. But we viewed the two local state comps. anyway, and both DD1 and us had a preference for one. She started there in yr7 and is now in yr9. On the whole, she is happier there. There have been issues in that where she was ahead she was allowed to get away with not doing very much work in yrs7 and 8, so consequently made little progress. She is still working well above average though, and has just chosen all academic options for GCSE.
Interestingly, whenever the subject of private / different primary schools comes up, it is DD1 that asks why she could not have gone to as nice a school that DD2 goes to. Where the teachers are friendlier and don't bully the kids!
I think there may be issues in the future if DD2 sits for grammar school in the neighbouring borough, as DD1 was not given the opportunity, but we have a couple of years to decide on that one yet.
Before all this happened, I very much favoured private education. Now I believe it depends on the child, and although DD1 got much out of it in the earlier years, ultimately the school she was at did not suit her. I think this is partly due to her being one of the youngest in the year. She is also quite painfully aware of the differences between her current and previous school, and realises she is possibly not receiving the education she could have had. She has recently asked if it would be possible to go back to her old school for A levels. Whilst we do not want to rule that out, it would mean losing the sibling link for DD2's addmission, which is no. 1 criteria.
To outsiders, it does appear that DD2 has got the raw deal. She never does any extra curricular activities, where DD1 did loads, and still does some. But we keep offering. Yet it is still DD1 who is highly jealous of DD2.