Your Motor home may have up to 4 cooling zones.. The DASH AC cools the "Cockpit" zone, (Driver's and passanger's seat and a little bit behind them) no way does it reach all the way to the rear of the bus. The rooftops cool,, Well, the entire bus. THus running the generator to run the roof top does a better job of cooling
Next is fuel economy. My Genset is a 5500, that makes the engine around 10HP, at full draw it's about 1gal per hour if memory serves (I have the chart here, that may be half draw) at idle it's about 1/2. However the engine AC is never on at half (yes I know you can adjust the temperture but the AC is either ON or OFF, no half about factory AC, Dealer AC on the other hand cycles on and off) I have found that extra power up front (Mine is a frount engine rig) means more gas millage believe it or not so taking a few HP off to run ac really cuts the millage.
Another factor,,, Someone said smaller engines tend to be more efficent... Don't know about that but I do know this, the engine on my ONAN is supposed to turn 3600/N RPM (Where N is likely 3 but may be 2) This really is etched in stone (Silicon to be exact, the control board for the generator) any faster or slower and things work, funny.
The engine on the MH is designed to work at many speeds. A constant speed motor is far more efficent, cleaner too