No, not "pretty much exactly". Private schools can basically pick and choose who gets in. Private schools don't have to deal with children who have problems. Public schools have to provide an education to every child, regardless of what problems and challenges that child might have. Once public and private schools operate under the same set of rules, then they can be compared. Until then, comparing public and private schools is nothing but a compassion of apples to oranges.
Private schools in Fl are dealing with kids with problems, and the turnaround for many of them has been remarkable. Nearly all the kids under the voucher program are the ones you described. A real curriculum, along with discipline and instilling work ethic, does wonders for problem kids, and even improves the parents attitude toward schooling.
It is a cultural thing, for sure, especially here.
That's why Fl (and other states should follow the example), offer parents the choice of getting their kids out of bad schools. A portion of the tax dollars paid, whether these parents pay any tax or not, is sent to these schools to get these kids out of the sucky educational environment they are stuck in.
The public school system would do much better to just get back to educating with discipline, not indoctrinating with all kinds of PC and feel-goodness crap.
The public school system should be the catch all, not the end all. All my kids attended public schools, and did just fine in the environment you described. We were not "unprivileged enough" to qualify for any vouchers for private schools, and I hold no grudge to those who can get their kids a better education with tax dollars, and the real opportunity to get out of their loser attitude.
The voucher program works here, and would work there, for those who really want to care and take advantage of it. The public school systems would be wise to let their counties and states manage the system, not the feds. If the states and counties continue to be stupid, well, you just can't fix that.
It all starts with voting.