I have two traditional brick "open" fireplaces in my tri-level. Burning wood in either one, puts out a pleasant dry heat in that room only, but sucks cold air into the surrounding rooms. I installed a gas fireplace insert in one, it heats that room and parts of the adjoining rooms. With the fan on, it is very warm, perhaps even too warm for that room. During a power outage it will heat that room, sans the fan (no power) very well, and some of the adjoining rooms to a much less warmth.
In the basement room fireplace, I installed a wood burning insert. I have lots of wood to burn, so I have a fire often when the weather cools, late fall and winter. I typically keep it burning for several weeks at a time, unless there is a burn ban. It heats that room very well, perhaps even a bit to hot. I especially like to stoke it at night, and let it burn all night. What this does is "pre-heat" the cold air being sucked into the central heat furnace, so it runs less often, and for less time. I save perhaps 10% every year on my heating. Probably after 20 years, it has paid the installation of the insert. When there is a power outage, (once for 2 weeks, but usually, only a few hours or a day) it is wonderful to have the heat, and it keeps that room toasty warm, and the rest of the house reasonably warmer than outside.
If your only concern is power outages, a better purchase than a fireplace insert would be a gas generator, perhaps whole house, like a Generac, that would allow you to run a gas furnace, and of course your refrigerator and some lights, maybe some electric heaters...etc.
Also remember if you don't have lots of trees that you can "harvest", you'll have to buy wood, which I think is more expensive than natural gas for the BTU's you get.
I don't have any experience with wood stoves, but I'm told they work pretty well heating a room/house, and are way more efficient than a fireplace insert.