In Starfleet's case, I think it would depend on how the Academy is geared toward producing officers versus enlisted so I can't say with any certainty either way. If O'Brien ended up on that ship, I think he'd still put Watters in his place somehow.
That has a lot to do with the ambiguity of how Trek treated enlisted/NCOs. O'Brien in particular. He was alternately portrayed as wearing one pip, two pips, one hollow pip, and then some funky chevron thing for most of DS9. Dialogue referred to him as Ensign, Lt, Chief, Petty Officer, and once as simply "Conn" (although that was Encounter at Farpoint, and he was a throwaway at that point). He was also mentioned as having attended Starfleet Academy, which no enlisted would have done, and served as Tactical Officer aboard the Rutledge. He acts as the Chief Engineer on DS9, which is confusing as a Chief Engineer is usually an officer, not an actual "Chief".
But in regards to putting Watters in his place, as a seasoned CPO he would certainly slap around Watters right up until the point where Watters issued an order, in which case he'd be obliged to obey it, albeit grudgingly. Young officers are supposed to heed the advice given by CPOs.