How old are your kids OP? Will you be able to afford private the whole way through for all your kids (bearing in mind that fees have been rising above inflation for years & now VAT on top)? What about extras like expensive trips etc?
Do you need wrap around care/the longer hours of private schools? Or do you want to be more actively involved in your child's day e.g. taking them to sports clubs, helping with scaffolding homework etc?
What are the state and private options in your area?
Do you want your DC to have very local friends that they can meet up with?
Do you have the capacity (in time and effort) to provide experiences that would round out a state school education? Clubs, learning an instrument, stage/drama classes? (We are lucky that locally the culture tends towards a lot of arts/drama/music opportunities in state primary, and also a decent amount in state secondary. I understand that this is not the case in many areas of England). Turns out my DC loves drama, and had the chance to take part in a number of performances (including national competitions) at primary. He wants to further pursue this at state secondary, and we also have an excellent youth theatre group locally which he can audition to join when he is ready. He's also really into sport, and we have been ferrying him to numerous clubs since he was four. His school has a number of teams for the main sports, but he is trying to set up a new boys' hockey team (currently only have girls' teams), and is being supported by the head of P.E. to do so. They are not so strong on minority/individual sports (athletics excepted), but do their best to provide support and encouragement.
My DC's school is not the best state option locally for academic results, but I discounted the most academic one for being pathetic at dealing with ALN (a form of underhand selection imho). We also looked at the very few private options available locally (and much further afield with a view to moving for his education), but they were either super selective, or a bit bumbling but traditional, or just run on a shoe string with exceedingly poor sporting facilities and at risk of imploding due to the (then upcoming) VAT changes, or put off by his mild but complex ALN. Also, they are businesses, and we realised the difference to LA maintained schools very quickly. Yes, state school bureaucracy can be a PITA, but you have certain statutory rights and there are processes that need to be adhered to. This is not the case with private schools. There are also cultural and language reasons for us to choose the local state schools rather than private.
I think there's a lot of things to balance in choosing a school for a child. Our DC was initially ok about moving to a secondary school which none of his primary peers would attend, but became increasingly upset about it as Y6 progressed. It looked as if it would be a bumpy transition, but has not proven to be so. So far he is much happier than he was at primary, and has made friends in class. He seems to feel that he belongs, and that is a really important feeling to have.