Since we know the coaches involved, we don't have to generalize. The 2007 38S diesel has a 31,000 lb GVWR and 41,000 lb GCWR, vs 22,000 and 26,000 for the gas Bounder (Workhorse W22). The diesel has air brakes and air suspension while the gasser has leaf springs and hydraulic brakes, but both have a solid (I beam) front axle. Both coaches have ABS. The chassis construction for each is pretty much the same - straight rails with 50,000 psi steel. Both have 6 speed Allisons, but the diesel has the industrial grade MH3000 while the gasser has the lighter duty MH1000. The diesel is a 7.2L Cat C7 with 300 HP and 860 ft lbs of torque. The Workhorse has a GM 8.1L with 340 hp but only 455 ft lb of torque. Both have 22.5 inch tires, but the Workhorse tires are slightly narrower because of the lower GVWR. The diesel has a 55 degree wheel cut while the gasser is 50 degrees.
So what does all that mean? The diesel will turn sharper, pull grades better and with the engine in the rear it will seem much quieter to those in the cab. Probably get slightly better fuel mileage too, though not enough to celebrate about. If I liked both floor plans, I'd probably take the diesel cause I'm a guy and like lots of power. But when the annual maintenance bills rolled in, I might have a few wistful moments...