The only issue I have seen is that with my EAN cert, a certain dive shop will not take a certain large certification agency's card for fills. However, I don't need to show that card anymore, because I have one from a different agency. I do believe that is unfair, they look at that agency as being sub-par with training. Even-though the curriculum is the SAME between both agencies, and when I took the "class" with their "poorer training company" my instructor covered mixed gasses with far more depth than the instructor with the "better" agency.
That is the only time I have seen a DS turn down a card. As others have said, PADI is in fact huge. A buddy of mine has his GUE card turned away for and "advanced" dive in Thailand. We all had to sign wavers for a dive that was less than 60 feet since we only had OW cards on us. I believe this was mostly because the DM was an intern, and was concerned with legal issues if we got hurt. Once the first dive was over, he felt quite confident we could handle any dive he could find.
With all this being said, I would bet most shops anywhere in the world will take your NAUI card. I would recommend getting an AOW too though. DM's tend to think of you as a much better diver with it so you get better dives with less coddling.