Depends what you want. I have a talented cousin excelling on the sporting programme. Her brother is ticking over but not setting the world on fire but both have the same schooling opportunity.
An ex was moved from state to private as he was in with the wrong crowd using drugs. He said the private school had better and greater availability of drugs and it went further under the radar (coke at private vs weed at state).
Another friend was moved to private away from rough state school friends. So you can expect a few wild cards but this may be significantly tempered by a private school having more authority to expel those kids if they cause hassle for the school.
I out earn 6 of 9 private school friends. But some of those dont need to work.
1 was sent because of the boarding opportunities for the parents.
Another was well supported and now has a very niche job.
So it depends what you want from it. It doesnt guarantee a good life but it can certainly offer opportunities for the Arts that state schools can't come close to and ensure better classroom behaviour and therefore better access to an education, especially as many parents consider themselves to be paying for top grades. It's what your kid does with them that's important.
Unless it will tip your kid into top marks or Oxbridge, you need to ask yourself whether the money is better spent in supporting them in other ways. If your kid is not naturally academic, being around highly academic kids that find the work easy may be harder for them.