The agency vs instructor is only somewhat true.
PADI has a very strict set of rules regarding what can and can't happen in their classes. As such, you can have a phenomenal instructor that is extremely restricted in what he can and can't teach. Advantage is, no matter how ****ty your instructor is, you're bound to do the same stuff that a student with the awesome instructor did.
NAUI has 0 rules regarding how the classes are taught. They have a set of stuff you have to do, what order you do them in, and how you get there is up to the instructor. One is demonstrate neutral buoyancy. While in PADI that may be just inflate your bc till you hover for a bit, we make them approach a weight belt, hover over it, ascent 10 feet, hover, come back down, don the weight belt without touching the bottom, ascent 10 feet, come back down, get rid of the weight belt, and turn and come back.
We have good instructors. A crappy NAUI instructor obviously may not do that, but the option is there to teach however you want.
Personally, if you want to be an instructor, I think AOW and Master Diver are a waste of time, but that's just me. We do OW then Rescue then leadership stuff. Our Rescue class encompasses a deep dive and a night dive, so you get the experience, and then we just encourage you to dive more. Sure a charter might want to see those cards, but if you show up with Rescue Diver that's usually sufficient. Getting to Dive Master after that is pretty simple as well.
key points
Crossover is good, at least for different instructors-gets rid of the "Scuba-God" mentality about your OW instructor
Different organizations doesn't matter. There's crossovers for instructor level too, so it really doesn't mean a whole lot if you bounce back and forth between a bunch of different organizations in the beginning anyway