I am not familiar enough with NAUI certifications to be entirely sure, but if you are NAUI Advanced Scuba Diver, plus you have the NAUI Scuba Rescue Diver qualification, plus enough logged dives and your qualification in CPR is less than 2 years old, you may well (just as an example) be able to join the PADI Divemaster course, which is one of the next levels (the other being PADI Master Scuba Diver) after the PADI Rescue Diver; and for me that means that, formally, PADI assumes your cert is equivalent to PADI Rescue Diver (if I understand right; I am no talking on behalf of PADI here). From the PADI Instructor Manual (I translate from my French version of this manual):
"To join the PADI Divemaster course you must :
- be certified PADI Advanced OWD or an equivalent recognized certification, ie proof of a certification above entry-level and at least 20 logged dives showing experience in underwater navigation and deep diving (18 to 30 meters)
- be certified PADI Rescue Diver or an equivalent recognized certification, ie proof of a qualification in diving rescue by an agency other than PADI
- if the candidate fails in demonstrating a satisfying rescue during the PADI Divemaster course, he/she will have to follow the entire PADI Rescue Diver course
- ... (etc)."
In other words, and generally speaking, PADI is happy to integrate within the PADI training system, at the level corresponding to their abilities, divers certified/trained by other well established agencies (eg NAUI).
Anyway, if it's just for fun diving, the NAUI Advanced Scuba Diver + Scuba Rescue Diver certifications will be more than enough to dive with a PADI Dive Center everywhere in the world (and with these certs you should be allowed to go down to 30 meters, in most countries; and down to 40 meters with a "deep" specialty if local laws allow that depth).