I've been certified by both NAUI and PADI, the latter more recently because my NAUI cert. had lapsed and I was in an area populated by many PADI shops, so I just went with the flow. I think the most important difference is the instructor REGARDLESS of who the licensing/certifying agency is. I had a NAUI instructor who gave me a course just short of SEAL training it was so tough. By comparison, PADI was much easier, but I switched to a different PADI instructor on my second day and this guy was no slouch either, which made me feel safer and better.
SCUBA diving is not like skateboarding or skiing, if you "fall down" you better know what to do because you only have seconds in which to do it, the right way, the first time. So if your training facility keeps saying "we make it easy", run - don't walk - to the exit.
Granger