In terms of the engine type itself taken in isolation, there isn't a vast difference overall. A diesel engine will get somewhat better mileage per gallon, in no small part because diesel fuel has a greater energy density (and, not coincidentally, density in the ordinary sense of mass per unit volume).
However, for class A motorhomes, there are many other differences that also almost always come along with the engine type, even though they are not inherently related. Gas motorhomes are practically always front engine units, usually built on the Ford F-53 chassis, with a leaf spring suspension. Diesel class A motorhomes are practically always rear engine pusher designs, usually with air suspension, and often larger and heavier and more upscale than gas models. The rear engine makes for a quieter cockpit area when on the road, and the air suspension a smoother ride. The lack of the engine in front can also make for a roomier or more open cockpit area, depending on the specific design. On the other hand, some gas motorhomes have a large storage compartment in the back that cannot exist with a rear engine.
Maintenance costs are probably a little higher for the diesel units, often because they're bigger and heavier and may have more complex systems. Larger tires, for example, are significantly expensive than smaller ones. The diesel engines typically have longer scheduled maintenance intervals, but when required the maintenance tends to be more costly, so the expenses end up being more "lumpy" over time.