This was discussed on a question I posted about 3-4 weeks ago about what is better to run a refer on. In theory, if you are getting 120 volts AC and no voltage is lost due to drop in the cord, electric and propane should cool down the refrigerator exactly the same.
I mainly use propane because a refrigerator uses very little, it keeps the spiders out of the flue, and if the electric isn't exactly 120 volts, it cools things down a tad better.
As for cooling things down, I like tossing the hard packs of Blue Ice into the refrigerator, and one in the freezer, mainly to keep frozen items cool for the 2-3 hours until the freezer is cold enough. The refrigerator will take a little longer (although a tiny battery operated fan does help.)