#1 factor in student success is parental involvement. The kids that escaped the LA schools are the ones with parents that cared enough to get them out. That raises success rate of the private school and removes the students who were most likely to go to college from the public schools, further driving down their %.
The private schools don't have to deal with the bottom 20% or so of intentional non learners that the public school does. This will also distort the numbers.
All that being said, I'd be moving heaven and earth to get my kid out of there.
I make a distinction between Catholic schools and secular private schools. Catholic schools incorporate religious faith and spiritual ethos. They are not merely private.