I have owned cat and noncat stoves on the same hearth. I also currently own one of each. We heat 100% with wood in WA at nearly 1000' ASL.
The cat stoves (BK or Woodstock are superior to the others) are fully capable of a flaming fire just as long as any other stove but to get flames you will not be burning at the very low burn rate. Noncats are almost always flaming because they are unable to be burned at such a very low burn rate without polluting the world with smoke. Efficiency between the technologies is not terribly different with an edge to the cat stove. The biggest upside to a cat stove is the very wide range of available heat outputs so you can have a very low burning fire for 30 hours or a very hot burning fire for 10 hours. At the low end, no flames, at the upper end you get flames.
Operating the BK cat stove is very different than a non-cat like your Jotul. You load the stove to the roof, get the fire going, engage cat, set thermostatic intake, and don't do anything else for the duration of the burn which is 10-30 hours. Only the BK has a thermostatic intake but even without it, there should be less fiddling that you're used to.
In Idaho, Kuma makes a big cat stove that is very efficient. Needs an 8" flue though. The rest of their stoves are ho-hum.
https://www.kumastoves.com/Store/ProductDetails/sequoia
If you do go non-cat, don't waste your money on an expensive stove. The NC30 is a beast and really leaves nothing to be desired. Ask yourself, what do you get when you pay 3-5 times as much for a competitor's plate steel stove? I'm super critical and see very little room for improvement with the NC30. I like it so much I bought a pellet BBQ from the same brand.
I've owned a hearthstone non-cat stone stove. The stone is marketed as a great material and it does look great. It's a crappy material to build a stove with though. Takes forever to heat up. The cat stoves with stone are meant to be run 100% of the time so you minimize the warm up drawbacks.
Your thread questions are very loaded and lots of opinions will exist. You asked the cat vs. non-cat question which is often a big debate, you asked the stone vs. steel question which is another frequent debate.
I think we all can agree that you need a big stove. Nothing smaller than the 30 series BK stoves. You are trying to be 100% wood heat in Idaho probably burning doug fir. You need a lot of available heat.