Other than the cost the only downside I can see is they mix with a more narrow section of the population - this can also be a positive though.
I sent my kids privately all the way through. It was worth it for us, and the best decision we’ve ever made. We were in a position though that it was walkable from our house and we could afford it without giving up holidays etc.
Positives for us were - small class sizes, high academic standards, varied sporting, arts, music and language options, specialist teachers for IT, music and languages - genuinely something to nurture the talents of each individual child. Also high expectations for manners and behaviour etc. and great facilities that unfortunately state schools can match.
The also provide great wrap around care 7:30-6 if needed and holiday clubs to cover holidays that aren’t state school holidays if you need it.
We also found the pastoral care fantastic as as the class sizes are small with additional TAs any areas of struggle academic or social were supported quickly. One of mine struggled socially (nothing major) but they helped her talk about her worries and build great friendships. There is also zero tolerance for bullying and that makes it a much more pleasant environment.
The children came from a diverse background but with parents who signed up to the positive ethos, being involved and valued education.
Lastly for us it took all the stress and worry out of years of tutoring or prep for the 11+ as this was just part of school and they knew nothing about it. This in itself was worth every penny compared to the stress I’ve seen some 9-11 year olds under!
As a previous poster said I have also heard primary school teachers say that private at primary is more important than at secondary - to give them an excellent foundation. I really have found this.
The confidence in public speaking, being themselves but kind and caring, giving back to the community has been great. But for me the key thing is that they develop a love of learning and a desire to get involved in all sorts of things along with a belief that if they work hard they can do anything has really set mine up for success in later life.