Here is some simple math to settle the agency debate
PADI = NAUI = SSI = PDIC = YMCA = _____ Fill in the blank. They all follow RSTC standards and generally speaking the academics and skills you learn will be the same. Breath in - Breath out, go up and down, clear regs and mask, inflate and remove/replace BCD's and weights... etc...
As others have already pointed out ... this is not accurate. Although NAUI was one of the original members of the RSTC, they have not been a member for quite some time ... and do not "follow RSTC standards".
Also, you need to understand what "RSTC standards" means ... it's touted as a set of standards that all members must follow, but in reality it's nothing more than a "least common denominator" of the standards that have been independently adopted by each of the member training agencies. In other words, those standards were "reverse engineered" to conform to what already existed. In that respect, they are so low as to be meaningless.
Here is the math you need to consider
Does Instructor A = B = C = D?
The answer is not always the same. The agency does not matter nearly as much as the Instructor... and to some degree the dive shop they teach for. The dive shop can be a factor because they may or may not hold Instructors to high teaching standards, gear used for classes may not be in good repair etc...
Yes this topic gets debated over and over in threads. Why doesn't someone on SB put a permanent thread at the top of the page to thwart the need for constant reiteration.
To a degree, yes ... the instructor makes more of a difference than the agency. But there's an equally important part of this equation you missed ... the student.
There are some very real differences in how the same topics get presented. PADI tends to focus on the "mechanics" of diving ... the "how to". NAUI tends to focus on the "physics" of diving ... the "why". Ask a PADI instructor about buoyancy control and they will most likely focus on the manipulation of air spaces in your BCD or drysuit. Ask a NAUI instructor the same question and they'll start the conversation with a description of Boyle's Law. Which is better? ... depends on how the student best understands the concepts.
PADI's class is very structured ... and for the most part you MUST teach things in a certain sequence and a certain way. NAUI's class is less structured ... and as long as the instructor covers all the required subject matter they are free to structure the class as they see fit, and add or enhance on topics they feel are important to their local diving environment. To a degree, PADI instructors can do that as well ... but they are not allowed to pass or fail the student based on that additional material. PADI says if the student successfully completes the required material, you MUST pass them. NAUI says that the instructor can (and should) use their judgment, based on a subjective "loved one" standard. Which is better? ... depends on the student, more than on the instructor.
Both approaches have advantages and disadvantages. But it's not just the agency ... and it's not just the instructor ... it's also the person taking the class. Some people are very "hands-on" ... if they can see it and feel it, they understand it best. Other people are very "intellectual" ... if they can understand the theory behind it, they understand it best. Which approach works best for you depends on ... you.
... Bob (Grateful Diver)