What are the pros and cons of a Diesel over a gas motorhome?
Well, the diesel engine is part of it, but just one piece of "diesel pusher" vs a gas motorhome.
Diesels are used on larger/heavier rigs because it is the more effective way of moving big vehicles. Much has already been said here about engines and fuel, so I'll move on to the other aspects.
DP's have air brakes and air suspension. Air suspension is superior to leaf springs for ride comfort ans well as being auto-adjusting for changes in weight and weight distribution. Air braking has some technical advantages as well, so is the system of choice for very large & heavy vehicles.
A DP chassis is invariably designed to be more rigid and with greater weight capacity (GVWR & GCWR). Some of that is because the diesel provides better low-rpm power, but some of it is simply that its a higher priced chassis that can bear the extra expense as part of the coach price (see below). DP's enable the use of heavier components, e.g. real tile floors, solid wood cabinetry, larger appliances, bigger water tanks, etc. Gas coaches max out at 22k-24k and 38 ft, so larger rigs with more amenities and upscale components are invariably diesel. You can have a few of the nice things in a gas rig, but you can't have them all because of weight and length considerations.
Because the diesel engine is so expensive, it pushes the coach into a higher price class. Thus, motorhome builders tend to put the other more expensive design attributes and components along with it. There is a lower end to the DP price scale, of course, but they generally still are better equipped than many gas chassis rigs. DPs generally start about where gas chassis coaches leave off.