If you have a large source ( residential size tank ) of propane and a moderate gen/fuel need, then propane is a fine choice. Propane has difficulty in cold weather sooner than properly treated diesel. Small tanks, <100lb, have difficulty giving enough vapor at temps of -30C or so and below. Diesel is fine down to -40C if proper winter fuel is available, all water is eliminated from system, and fuel is treated to prevent waxing of filter. Gelling is not usually a problem, waxing and any water always is. Gasoline wins for coldest weather, but is the least safe option.
I'm thinking propane gen set has cheaper up front cost per kw.
If cold is not an issue, then fuel availability and transportation ease, cost, will help you decide. For us a trip to town for anything is a 4hr time commitment, no delivery of anything out here.
Diesel is beast for longevity, however, propane runs very, very clean, engine oil stays cleaner far longer than with either diesel or gasoline. Seems good to me. We have a 6kw liquid cooled Honda gen set converted to propane from day one 25 years ago. Light usage, excellent results. To attempt to compare fuel consumption without exact side by side comparison seems a bit shortsighted.
Current crop of quality inverter/generator sets, 7.5kw+ either fuel source, would likely show THD<5%, w/stable or adjustable voltages. How much better do you need. They also derive their current mandated efficiency from complexity, just like an auto. Not as easily repaired as they used to be.
'Clean' pure sine wave power and auto start are great, but probably double the cost of your inverter.
High quality deep cycle batteries are cheaper per delivered kwhour/charge cycle of usage than any 'dual purpose or RV' battery. Best way to shorten the lifespan of any battery is chronic undercharging, and a generator with some little battery charger is the best way to ensure you recycle your batteries early. The harder you use/load your batteries, the better your charge system needs to be. My old Trace SW4024 cleans up and makes good use of 'dirty' generator power, I would not consider charging these batteries in any other way and we run all our house AC needs through it.
We do exactly as was mentioned at times. My 4.5kw Cummins/Onan delivers 20+ amps to an L-16 battery bank that would like to see 40, but we run it to take the occasional heavy load off of the system. 15-20% less power on propane than gasoline, believe. Another 1200w of panels/controllers if I made the space w/daylight usage, would be far cheaper and more cost effective long term than the 7kw generator/fuel I would need to get those 40 amps. That gen set would also cost 3-4x the 1000.00USD I paid for that efficient little Onan.
We get along by not needing power and by giving in to gasoline/propane generators for my welder and heavy/non-battery power tools. Simple.
Don't forget, cold ( well below freezing ) solar panels deliver as much as 20+% more voltage (not amps) than warm ones. that's real power if your MPPT controller can make use of it.
My south facing front yard slopes down to a 400ac lake that freezes over in November. All that snow, Nov. to Apr., means my solar gain is not as diminished by winter days as a lot of folk's.
Been off grid part time/most time in B.C. for about 30 years. That's my experience.
Not enough information in the original question, why the thread answers are so varied.