The advantage of the 240 volt outlet.. Assuming it is wired like I think it is. (120-120 or 240 across) is that the neutral wire carries no or less current.
Imagine you have ONLY two identical Air Conditioners running
Current flows up L-1 (With the associated voltage loss) and and back down L-2 (Again with associated voltage loss) To make the math easy let us assume 1 volt. NOTE 1 volt is just to make the math easy.
THe result is each A/C is quite happy with a precieved voltage of 119 Each>
Now let's use the 120 volt outlet.
Each leg, in the motor home Still carries the current for ONE A/C with the associated 1 volt loss.
But the NEUTRAL carries the current from BOTH with .. as a result. 2 volts loss And in addition it is now carrying more current than it is designed for (Fire Danger).
So the A/C's now see 117 volts.
And this is why houses are wired 120/240 as well as 50 amp RV's