So the answer likely changed during the period. You can look at the earlier paintings done by Morier for the Duke of Cumberland, and they all seem to show an epaulet worn on the left shoulder to secure the cartridge pouch belt.
Early in the AWI, the clothing of the coats likely reflected the fact that many regiments wore their bayonet belt around their waist, but this quickly changed to them wearing them over their shoulder. This move likely resulted in changes to the uniform, perhaps unofficial at first, but likely done on purpose shortly after. This "extra" epaulet helped secure the bayonet belt. The other parts of a soldiers kit – knapsack, haversack, and canteen, were often dropped when going into combat, so a soldier would not want to fumble around with unbuttoning their epaulets then.
The officers epaulets are a bit more confusing. Most line officers (of hat companies), only wore one epaulet on their right shoulder, to secure their sword belt. Grenadier and Light officers wore two. There were a few regiments that wore two regardless of being a hat or flank officer, but I'd had to do some digging on that as I don't recall off the top of my head which ones.
Note that Majors, Lt. Cols, Cols, Brigadier, Major and Lieutenant Generals in the British army also wore only one epaulet on their right shoulder (regardless of the incorrect sculpting on figures). It was only full generals and the Field Marshal that wore two epaulets during the AWI – none of those in North America.
I'm both a re-enactor (British), and wargamer. Hope that helps. :-)