I've taught with both organizations for 17 years. I'm not active with either agency at this time and teach through ACUC, CMAS and DCBC/IMCA, so this is more of a historical difference than a current one.
I believe that the quality of the training delivered to a student is a result of the Instructor more than it is the certification agency the Instructor teaches through (with some exception). That said, I believe that PADI places more restriction on their Instructors.
PADI tells the Instructor what to teach, what to examine on and viola, a certified diver emerges. Although the PADI Instructor can add to the program content, he can't withhold certification if the student fails everything that's added. If they meet minimum standards, they get the card. This is not true with NAUI.
NAUI Instructors are encouraged to teach beyond the minimums. Anything they add is considered on par with NAUI standards. They must ensure that the minimums are met, but can withhold certification until they are satisfied with the divers performance and successful completion of
all requirements.
In other words, regardless of the minor differences in the program, PADI Instructors are more limited/restricted than a NAUI counterpart. A PADI Course is what's in the book. NAUI cannot be accurately defined as it's not limited to the standards. A student may learn as much on a PADI program, but they don't have to. With NAUI it's up to the Instructor.
PADI has a superior business model. They are the McDonald's of diver certification. You know what you get anywhere in the world. They have excellent quality control and even the idea of the PIC was in-place in the early 70's. PADI is all about business and making money.
For me, NAUI is about quality. PADI split-up the diver program into tiny pieces that allowed more certifications to be completed to achieve the same goal. More and more, PADI continues to pair down the standards (buddy breathing for example). NAUI's standards have dropped as well. If you're in the same business, it's hard to beat McDonald's. NAUI have been left behind in numbers for this reason.
NAUI is run by its members. PADI is a for-profit corporation that has none. An image is projected that you're part of the PADI organization, but in reality your not. Having a PADI Facility is the same as a Saturn Dealership. If GM wants to cut you off, your out.
I had both a PADI Training Facility and a NAUI Training Center. I was a Course Director with NAUI and a MSDT with PADI. PADI wouldn't allow me to have a 5 Star Facility because I taught other programs. They also wouldn't allow me a certification higher than what I had unless I took the mark of the beast.
NAUI on the other hand wasn't concerned about me being an Instructor Examiner with other organizations. With PADI it was about control.
PADI has always had the lowest standards. A PADI OW Course use to be 27 hours minimum, NAUI was either 34 or 35 hours (it has been a few years). The NAUI Instructor course was much more difficult than PADI; again higher standards.
Hope this helps.