Some advantages/disadvantages with either one. LP stores better, but in very cold weather, it won't liquify from a small tank. Some claim that LP causes some HP loss on their generator or they get less running time from a 5 gal LP tank than they do with 5 gal of gasoline (I haven't noticed either of those, they seem the same on both counts)
I don't usually keep more than 10 gallons of gasoline on hand through the winter (but I do keep both vehicles topped off, just in case), but I do keep 4 20# and 2 30# LP tanks on hand and topped off prior to the winter season.
A few years ago, we had a freak windstorm roll through here and knocked out the electricity county wide, we had no electricity for 7 days, other parts of the county got theirs back after 3/4 days. None of the gas stations here had generators at that time, so they couldn't pump gas or even use debit or credit cards, but if you had cash or check, they'd unlock the cage and go the LP tank exchange route, but that's fairly expensive.
If you do buy one of the LP kits, make sure you get a dual fuel kit so you can run on either LP or gasoline.