My wife had to go private. Being white in a predominately black area, in reality there was discrimination and difficulty the inverse of what is typically discussed CONUS.
She got a high quality education and has done well from it. But in the end all, I wouldn't call it any higher quality or superior to what is typically produced in a decent district in NJ. Granted, NJ sets the bar, so there are reasonably high expectations compared to other places.
We bought for the schools. And while taxes are high, what we would pay for private school, for the duration, would be substantially higher than what we pay in taxes. You may or may not recoup it over the course of a lifetime, but there are too many variables there.
But in the end, its not what state/district/public vs private in any form, as much as it comes to how good your parenting is and how big of a role you take in kids' education. Schools, public or private, are not babysitters. Take the bad options (dangerous, durg/gang filled, etc) bad schools out of the picture, and look at any typical American school system, and the outcome is likely much more dependent on a pupil by pupil basis on parenting.
Ive known some very smart people who didn't amount to much, and some very average ones who have applied themselves and done really well.
What do they say? The A students end up working for the B students, whose CEOs are the C students... Or something like that?