Some differences between PADI and NAUI courses, that I am aware of:
PADI Open Water- 4 checkout dives
NAUI Scuba Diver Course- 5 checkout dives or 4 dives and 1 snorkel (I just do 5 dives)
PADI Advanced Open Water- 5 dives (deep, night, nav req'd, plus 2 electives)
NAUI Advanced Scuba Diver- 6 dives (deep, night, nav req'd, plus 2 electives)
PADI Master Diver- 5 Specialties and then pay for the Master Diver card (I believe)
NAUI Master Diver- A course requiring 8 dives (deep, night, rescue, navigation, and search and light salvage req'd, plus 3 elective dives) and several classroom sessions ranging from physics, physiology, seamanship, etc. This course can very much be tailored to the Master Diver candidate by the instructor, provided the req'd dives and academics are covered. Much of this course was very similar to the PADI Divemaster course I took a few years ago. The final test is very comprehensive and challenging.
This is just my own personal experience from assisting probably around 30 classes or so as a PADI Divemaster before becoming a NAUI Divemaster and eventually a NAUI instructor. The NAUI Divemaster is the equivalent of a PADI Assistant Instructor as well.