There are some obvious "Apples and Oranges" issues going on here...
In comparing systems for heating, cooking, and other energy consuming activities, I made up a grid of what benefits each system could offer, and at what cost.
Diesel is already on board, requires no additional space for storage, and is not explosive. It can supply heat for cabin comfort, heat for cooking, and heat for domestic hot water. It can also supply pre-heating for the engine. Diesel furnaces are more expnsive, and will require some maintenance... service about once a year I am told.
Propane is likely the least expensive system to install.
It is capable of supplying heat for all the systems mentioned above, although I know of no-one pre-heating their engine with their propane furnace. (this should be easy to do) It does require tanks that come with a host of issues and special requirements, and if anything should crack or leak for any reason, you and your family could wake up dead. Alarms are mandatory, as are venting and care to keep all appliances in good working order. It is by all accounts a good value as far as BTUs per dollar spent, and you can power heat sources as well as refrigerators. (not nearly as efficient here though)
Batteries and solar systems are expensive and limited in their abilities.
They can be used for cooking, running pumps, fans, communication, and entertainment systems. Typically batteries are charged by running the engine, or plugging in to shore power. A solar panel simply extends the time interval between either running the diesel engine, the generator, or plugging into shore power. If battery capacity is great enough, this interval may exceed the duration of the camping trip.
Large battery/inverters systems offer the additional capability of allowing virtually any 110 volt appliance that can be envisioned including air conditioning and microwave ovens. Batteries and solar panels can both be easily mounted so as to not use up precious "living space". Solar panels are always mounted on the top of the vehicle, and batteries can be buried down in the "innards", particularly if they are the AGM variety.
You have to have batteries with either diesel or propane to power the various systems, timers, thermostats, etc. You don't have a choice in this. The question that remains is how often will you need to charge your house battery, and with what methods. You have an alternator on the van engine that is available, and maybe shore power, but maybe not...
Generators are powered with propane. diesel, or gasoline. The cheap ones are powered with gasoline, requiring separate fuel storage issues to be resolved. Propane generators work fine if you have already made the decision to install a propane system. Diesel generators use fuel already available in our Sprinters, but they are the largest, heaviest and most expensive of the three types. All are noisy and all require places that can accommodate the heat that comes with their operation.
Assuming an inverter, a generators only function is to charge the house batteries. Vehicles without an inverter will essentially only use the generator to power the air conditioner.
There are many ways to skin the proverbial cat, but in consideration of the above, I chose to go pretty heavy on the batteries, with four big ones, and to supplement their charging with solar panels. I'll forgo the generator and propane system, and rely on my superior planning to be where it is sunny when I am on vacation. If I am lucky, I should be able to camp without running the van for several days at a time in the sunshine. If it is raining, then I am going to charge the batteries with the van on my way to where the sun IS shinning!
I'll cook with either an induction cooktop, or microwave when I am inside the van, and hopefully enjoy grilling over a campfire when I have indeed been able to correctly anticipate the weather. Since I anticipate using the van for mostly one or two day jaunts, I doubt I'll need to worry about running the batteries low even in rainy conditions. In any case, with good monitoring equipment, I have lots of options. If my solar system can generate it's rated capacity for four hours a day, and I use twice that per day of camping ... I can stay in one (sunny) place for over five days without starting the engine. (I can use 4200 watts per day at that rate.) Without the sun, I am a two-day weekender.
So, how are you gonna skin YOUR cat?