The structure of the course was similar, with similar types of dives, but the NAUI instructor was very specific on what to do and worked very specially on technical things like kicks, trim, hand control, and put a lot of time into what my daughter needed specifically for her to improve. I have the manuals for both and I don’t think they are really that different in the reading.
Hmm, we should do a poll on how many divers during their PADI AOW had their instructor:
*be very specific on technique
*worked "very specially" on kicks, trim and hand control, and
*put a lot of time into specific individual improvement
as you observed with the NAUI instructor.
I have only taken 9 PADI courses with different instructors and sat in on a few others, but what you have described does not describe any of them.
OTOH, the NAUI divers that I have seen have blown me away with their skills, especially back when AG was the Training Director. Back then, I could not tell a class of divers completing their Master Diver course apart from GUE divers on the same boat. NAUI divers that I see consistently have very solid skills.
There are some PADI instructors who produce proficient, capable students, but some agencies instructors consistently produce proficient, capable divers.