There are good and bad private schools (I believe some worse than good state schools), and yes, money does not always guarantee a good education
But it may at least afford your child the best opportunity for one at the the top of the range - for example,
I recently went to an open day at major public school with my DS.
Admittedly I'm sure they chose their most talented pupils to present their musical/sporting/academic achievements, but it was evident the extra curricular/ academic opportunities and facilities were amazing.
At the end, we had a tour from a random (polite) young boarder. I asked him where he was aiming for after leaving school and without hesitation or a hint of arrogance he said "Harvard".
He had already discussed it with someone the school had hired as its Ivy League co-ordinator with links/expertise/inside track to help stiudents eg SATS/building experiences for personal statements and were forging close links with US universities.
Of course there may be state schools like that, - but not any that are local to me.
Is it a level playing field compared with the local state comp. Of course not.
So is it worth paying 30+ k a year for compared to a free education at the average or even best local state school ?
Well, I'd say you'd be paying for lot more than pure academics (eg simply comparing A levels to local state grammar school, of which there is only one locally, vastly oversubscribed), as it's also about an ambitious peer group, sporting opportunities, acres of lovely facilities, breeding of the self confidence of "yes aim for Harvard" and presenting oneself well).
Finally, and something which seems to count more and more these days than raw talent (though I am sure many parents who turned up in Range Rovers who won't admit it openly except to their own ilk), it is also about mixing in a social milieu which will opportunities for DCs to build their future network.