DTT, What i would recommend, and i am by no means an expert, is that if you decide to go with a small generator 3k to 5k i would stay with gasoline. And it is difficult to find a ready made small dual fuel unit. If you are going to use a larger 5k plus sized generator i would go with a duel or tri fueled unit.

As far as which fuel would be more available after an earthquake, i don't know. If the roads to your place are passable, the propane truck will be able to get to your house and fill the tank. Or you can leave to go get more gas.

On storing gasoline i have not had any trouble. Are you storing any fuel in the shed now? Don't know if you need gas for the lawn mower or your dirt bike. The only way to know for yourself go to your favorite big box store and buy one safety can and fill it with fuel and stabilizer put it in the shed and check it on a regular basis.

I went with gasoline because i already needed to keep gas for other things, aside from the generators there is an air compressor, chain saw, weed eater, and i also keep 5 to 10 gallons of diesel for the lawn mower too. But the cheap plastic fuel containers did not inspire much confidence, if you leave it out in the sun for 10 minutes it looks like a beach ball and there was always the aroma of gasoline where ever the cans were stored. So i decided that i needed a better way to store gas because i need to have gas. I hope that makes sense.