Natural Gas vs. Propane Fireplaces
Natural Gas Fireplaces
Many homes already use natural gas, so this is a logical option if you currently have a gas main you could run an extra line from. A new line is usually fairly easy to install and is a cost effective solution. Using natural gas is safe and clean, emitting very few toxic byproducts in the burning process, and because natural gas is so light, it will dissipate quickly instead of pooling in your home or on your patio should a leak occur. Additionally, since natural gas is provided by your city via an existing line, you'll never find yourself without fuel for your gas fireplace just because your tank's run empty.
Liquid Propane Fireplaces
Propane is a very economical solution since you'll need less of it to produce the same amount of heat a gas fireplace can produce. This "green" source of fuel burns cleanly and super efficiently, so if warmth is your primary concern, liquid propane is worth considering.
Because liquid propane is a heavy gas that'll pool in your home rather than escaping upward, fireplaces using it do require a safety pilot light that can't be lit with a match. Liquid propane fireplaces use an electronic ignition system, and that means you need electricity to start a fire. This might make a propane option less ideal for you if you wish to use your fireplace at a primitive getaway cabin.
Power aside, propane is a very popular choice among many home (and cabin) owners since it places fewer restrictions on your fireplace's location; as long as there's room for a tank, it's likely a viable option - inside or out.