The AOW course is nothing more than broadening your knowledge on diving and getting a taste of a couple of the specialty areas of scuba. I don't think you are an advanced diver just by taking AOW. You get to be an advanced diver by getting more experience. The reason these dive shops and charter boats want to see an AOW cert. is so they know you received (or should have received) the training required to safely plan dives and to dive to depths between 60 and 100 ft. I think with NAUI, as AOW, you can go to 130 ft... I teach PADI, so I don't know that for sure.
Exactly! I think the AOW course offers a great "preview" of what you can get into with diving, but shouldn't be confused with experience. For a particular trip, an AOW cert + a certain number of dives would obviously be better, but again means nothing if all of said dives were in unrelated conditions. IMHO, dive operations should be more concerned with the type of dives that a person has done in the past instead of whether they are OW, AOW, rescue, etc. I've seen good divers (hundreds of dives in one type of condition) go someplace new and end up being very uncomfortable/unsafe. If you stick someone (no matter how good of a diver) who has only ever worn a 2mm shorty in a drysuit, hood, and gloves chances are there's going to be some problems.