I don't think many units (if at all) have "hard-and fast" priorities... it is generally simply going to be a case of the controller making a decision and recovering the aircraft as expeditiously as possible.
Grass may seem greener on the otherside of the fence from time-to-time; frankly it would make the ATC task that much harder to hold-off traffic, whilst feeding in another that had been granted priority simply for commercial reasons or because of its flight rules.