FWIW, some of my thoughts on the various agencies that I have had direct experience with:
NAUI: I certified as a diver in 2000 with NAUI because thats what my friend was certified to teach and we had no other options on the base that i was stationed on. As i was a newly minted flight instructor, I was obviously quite interested in the teaching methodologies used in diving as compared to flight training. One of the things that I was impressed by was the "Freedom to teach" philosophy that was, at that time, unique to NAUI compared to other main agencies.
In practice, this meant that, as long as the students were made aware of deviations BEFORE signing on to the course, you could include ANY additional skills / dives / entry requirements etc etc as long as you met and exceeded the published standards. This was at a time when , for example, the swim test had been cut down to a ridiculously low standard (my opinion only) and my instructor explained that the NAUI standard was X and he would be requiring more from us, and explained why. Also, he required us to do fireman lifts and carry our buddy 100m as an entry requirement. His rationale was that since we did almost all shore diving with little to no support elements, it would be good to know we could carry our buddy up the beach to the vehicle and drive him to the hospital.
There were many other examples, the take-away for me was that if you had a valid reason for adding something to the course, the students always had the option of going to a different instructor. None did.
Later when I certified as an instructor it was with NAUI and i continued to implement many of the same requirements as my instructor as I agreed with the rationale behind them.
PADI: In my experience so far, I have never met a PADI instructor who did not believe that they were giving the best possible instruction to their students. All those I have met have been committed to training and teaching to the highest standards. The problem is that we don't know what we don't know, and many of these fine people have been through the OW-Instructor sausage machine. The nett result is that their personal skills and knowledge outside of the course materials is totally dependent on how lucky they got with who their instructors were. This is not PADI specific, but I feel it is fair to say that the majority of young professional divers becoming instructors are doing it through PADI so the numbers get skewed fast. I have no personal experience of being inside the PADI system but many of my CD friends and regular OWSI find that it is more restrictive wrt teaching freedom than many other agencies.
RAID: When I finally took the plunge and got a rebreather in January this year, I looked around for a suitable agency to take my first course with. I then discovered RAID and so far have been very impressed. They have a very flexible instruction principle somewhat similar to NAUI of old, e.g. the book says to teach a "non-silting" propulsion method and all skills to be completed in trim and not touching the bottom by the end of the course. i can choose whether i want the students to have mastered frog and back and helicopter turns or not, I can choose what my definition of the limits for hovering are etc. their QA is also outstanding in that EVERY skill has to be signed off as completed by the Instructor as well as the student before cert. They require in-water hour minimums as well as dive numbers, so none of this 4 x 20 min dive and you're done.
UTD: i was invited to do the UTD IDC recently and completed it successfully. On a personal skills level the requirements are substantially higher than the other agencies and I found out exactly how good i wasn't on day one. The QA is superb with all dives being video'd (sp?) and in the case of the IDC sent to the Training Board for approval of the candidate before cert. I feel that the control of instructor standards with UTD is definitely the best I have experienced so far. For me the biggest bonus is that I can run a UTD course and certify RAID as all the skills are covered and no issues with exceeding the required standards.