Well his rank was Chief Petty Officer, this was stated directly in DS9. That would make him a senior Non-Commissioned Officer. Basically if he was in the modern navy he'd have stripes on his sleeve.
Though his insignia both in TNG and DS9 widely varied, leading to much of the confusion on the issue. The fact that he often bossed officers around didn't help any. I just figured Sisko firmly stated that O'brien answers to him and him alone.