You're right - the priorites are the same. In general rather than commercial vs private it's instrument vs visual. Put the VFR behind the IFR & he can judge his own turn-in & separation, even if it means orbiting or extending downwind. Put the VFR in first & you have to be sure you have sufficient room for 160kts vs 75kts. Misjudge it & it's a long old re-position for the IFR tfc.
There's a whole lot of other factors involved too, like pilot capability, a/c type. pilot's familiarity with the airfield, is there a constant stream of IFR tfc etc.etc.
Further away from the field it's a question of who will get there first. Best way to answer the question is to go visit the ATC unit in question. Bring biscuits!