Hi, there. I think you will find that if you plan your dives together and follow careful diving practices the nuances of your training differences won't be important. The physics of diving are the same for everyone. Both NAUI and PADI participate in the RSTC, the Recreational Scuba Training Council, which sets minimum training standards for certifying agencies. Review communication with your buddy before your dives, agree on hand signals, and focus on the basics. And have fun!
I would rather be ashes than dust! I would rather that my spark should burn out in a brilliant blaze than it should be stifled by dry rot. I would rather be a superb meteor, every atom of me in magnificent glow, than a sleepy and permanent planet. The proper function of man is to live, not to exist. I shall not waste my days in trying to prolong them. I shall use my time. - Jack London