Ambient temperatures make a big difference in how well a refer cools on either electric or propane, and that's temperatures both inside and outside the RV. The thermostat is supposed to cool to the same temperature regardless, but how much electricity or propane it takes to get to that temperature is what changes. And of course, there is a maximum temperature difference the refer is capable of holding.
People have noted that refers generally chill to their set point much faster on propane than on electric. Not always, just generally. But if a given unit is only capable of holding a 60 degree difference between inside the refer and outside it, and the outside temperature hits 100 degrees, it'll run continuously and only get down to 40 degrees.