Great question. It’s a question I asked before my first class. To PADI and NAUI instructors the difference is huge. PADI is more global and offers a very specific curriculum for each class. NAUI is based in the US and gives instructors more leeway in personalizing classes. Both are well respected around the world.
Here’s my analogy: Did you take CPR from the Red Cross or the American Heart Association? They are very different organizations but the skill is the same.
Look at student to divemaster ratio, especially in your open water class. Look at curriculum, facilities, and personalities. Have fun!