FWIW, when my sis-in-law transferred her kids out of Phoenix in.....maybe 2nd and 4th or 3rd and 5th grades, both kids were right on par with the public school. They went from Phoenix to Oak Chan, and when Oak Chan was reviewing in the beginning of the year, her son said that Phoenix hadn't even covered that information yet.
Now, I'm not saying private school isn't better than public, but I am saying that the curriculum is not as different as they would like you to believe. I think the big difference is the extra stuff at private school.
Well, my son is in Phoenix, first & foremost, for the 6:30 AM drop off to the 6:00 PM pick-up times.
That convenience with both parents working combined with strict sign-in & sign-out procedures also provides confidence that while he is small, he is safer from the "Girardo's" in our society than if he was walking to & from the local public school in our neighborhood.
I also feel with the smaller class sizes, he does get more "one on one" time with the teachers than he would in the public system, so for me, it is a worthwhile investment, and one I am happy I can afford to make, but in all honesty, is likely pushing my retirement age out 4 years or so.
As for your last point, well when I switched from ARC to CSUS after taking my first semester of Calculus at ARC, I was behind at CSUS because the order of chapters and topics was different and I had to teach myself a whole chapter on calculus with logarithms and natural logarithms to catch up, but then 1/2 way through the 2nd semester of calculus, I ran into a duplicate chapter from my 1st semester taken at ARC, so it was a breeze for me. Anytime you switch schools and textbooks, you can expect to encounter topics that may have not been covered at one school and were covered at the other school.