In most cases, it is the instructor not the agency in my view. Many of the instructors and dive professionals have multiple certs with different agencies. And it isn't always "easy cross-overs". I am not even a dive professional yet and I carry certs from two different agencies. (And yes, IANTD and SSI do teach slightly different philosphies) In some cases, for business reasons they choose on agency over another.
IE. We had a shop open up with a gentleman who was an instructor at the LDS that I use. He thought about SSI from what I understand, but SSI doesn't allow more than one SSI shop within a certain distance of each other and this instructor would have been opening his between two SSI shops within that range. So, he opened up as a NAUI shop.
Recreational diving doesn't change that much between the major agencies.
I have read comments on poor YMCA, NAUI, SSI, etc. instructors. I have read good about instructors from the same agencies. I have seen good PADI instructors, I have heard of poor PADI/ NAUI/ SSI instruction and seen the results with silted up quarries, dangling gear on divers, and people who can't control their descent enough to keep from damaging their ears. (I try not to observe those classes, I have enough to do to keep a good attitude.) I have seen PADI instructors who will tell a student to either come back or not get their card as they aren't confident in the students once they turn them loose. Keep in mind this is with somewhat limited experience in "dive politics".
If you are concerned about agency differences, the best bet may be to take multiple courses from different agencies if you feel that you are missing something. (Although my SSI Deep Diving that I have the books for reads entirely different from agency that I did learn to deep dive from.) But, PLEASE, if you find an instructor who works for you, I would encourage the diver to stay with that person regardless of affiliation.