There are planty of state schools that can support seriously brainy children. My friend's schildren went to state primary and both ended up at Cambridge doing Maths. Also, the new primary curriculum is more challenging than the old curriculum so comparing the two is like comparing apples and pears. Unless you have excellent teaching and know what the new curriculum entails, it is easy to think prep schools are better. Some are, but some are not. You do not always get what you pay for!!!
I too have expereince of both. The local small prep my DD2 went to was, frankly, useless above Y1. Brilliant for Early Years and Y1. Non qualified teachers, poor sports facilities, full of over parented whinging children, poor music, and very few bright children. The reason for this? They were all in the much better state schools. Teaching was average to say the least and teachers could not control 15 children. This is why they were not teaching in the state system - just not good enough ! SEN provision was woeful.
DD then went to a top performing girls' prep school and that was brilliant. It did follow the national curriculum but it had specialist teachers and an amazing array of extra curricular opportunities and art and music that were brilliant. No other state school could match it, but it was expensive and took children to 13, not 11. It was full of pretty bright children despite there being no entrance test and every year children won academic scholarships to big name schools. I would therefore say, do not be swept away by a comfortable little school. It may be very average. Look at the destinations of the children. Where do they go afterwards? A small senior school is limiting and the same friends for many years is not particularly desirable. Changing at 11 or 13 is a lot more sensible.
My other DD stayed at the local primary school and thrived, but she could have achieved more there, had she been asked to. There were other schools that were possibly better, but we could not get into them! I think if you have excellent state schools nearby, you will find there is very little difference in the curriculum between state and private but less SEN and lower achieving children at the private school. If you have friends that are spread out over a larger geographic area, then you still make sure your child sees them. They just may not be able to walk down the road to them.
It is far better, in my view, not to use an average private primary. If you are paying, go for the very best school for your money. Secondary is the biggest problem. If you have truly awful ones nearby, then save your money for this. My state educated DD flew into an academic boarding school. She was in the top 4 re GCSE results and, she had never done a single MFL at primary school, but has a degree in two now. If you get the right senior school, your child will do very well and may well surprise you!