Naui vs Padi is a big question among American SCUBA divers. Naui and Padi are both organizations that offer certification for SCUBA divers and teachers who graduate from schools that are accredited by them. Padi is the largest SCUBA certifying body worldwide with half of all SCUBA teachers registered with them. Naui is popular in the USA because that is where it is based.
If you like to travel worldwide, go SCUBA diving and teach it, Padi certification and membership might be the way to go. Your membership will be respected throughout the world. However, even though Naui stands for the National Association of Underwater Instructors, they also say that they are the most respected SCUBA organization worldwide.
The fact is that, nowadays, both Padi and Naui are honored around the world. The main difference according to many instructors is that the Padi curriculum is more structured than the Naui curriculum. Naui instructors have a little bit more leeway to add personal experience and know-how to the curriculum. Padi instructors don't always follow the rules, however. Therefore, this difference is not a huge factor.
If you are really stumped in deciding Naui vs Padi, you may just have to research the diving centers that you will be taking classes at. Research the center, the curriculum and the instructors for each program and decide accordingly. Many diving centers offer certification with both Naui and Padi, which means that a Padi instructor will keep in mind that you may be going for a Naui certification and vice versa. The distinctions between the certifying agencies are becoming increasingly blurred in most schools.