We have a diesel pusher with a diesel generator and it makes sense to me to have them share a fuel source, notwithstanding the design limit that will not allow the diesel generator to source fuel when the tank is less than 1/4 full. Ask me how I proved that.
For me, that's a 100 gallon fuel tank, so the math problem is solved knowing the generator will take something less than .75 gal an hour at full load to run.
Many variables here, which include your limited fuel supply, the number of hours you need your generator, and the load you put on it.
Since mine came the way it did, I had no decision to make, and I cannot to speak to LP generators as better or worse from experience. Most of this is just a math problem, but I feel sure some LP folks will share their experiences. In my logical mind, I would think it easier to acquire diesel than LP way out in the boonies, but I could be way off base there. You can always jerrycan a solution for a diesel, but I suppose you could portable tank a solution for LP.
Informed minds will prevail.