If you look at the big 4, Wyoming, Montana, Alaska and Idaho there is no clear winner.
Wyoming and Alaska don't have state income tax. But they have taxes for everything else.
Montana has no sales tax, but they nail you in the rear end on everything else. It changes regularly but I think Montana has the lowest across the board impact to the individual tax burden of any state.
Idaho has a fairly low total tax picture.
For veterans there is not a clear winner. There is no single resident veteran program in one state that is better in another. None of them are Texas with tons of great programs, none of them are like Vermont with no programs.
Weather.
Alaska is either really cold, really rainy, really snowy, or really really cold.
Wyoming is either really cold, always really windy and really hot and dry.
Montana it depends on which side of the state you live on. It is either really snowy, really cold and if you live in eastern Montana really windy.
Idaho gets a lot of snow in the mountains, and a lot of wind in the desert. Yes it is still cold.
Fishing winner Alaska, edge Montana and Idaho over Wyoming. Alaska has something like 14,000 miles of coastline with halibut and king crab in the briny deep. Plus king salmon. Kind of hard to beat that.
Upland winner Montana or Alaska, then Wyoming and Idaho.
Waterfowl winner Alaska, Montana and Idaho way over Wyoming.
Access.
Alaska is the best and worst because the best areas are fly in or boat in. If you have the financial means Alaska is great.
Wyoming has a lot of locked up lands, so does Montana and Idaho.
Cost of living.
Housing in Anchorage, SE Alaska, Wyoming, Boise, Idaho Falls is all really expensive.
Housing in Fairbanks, Wyoming crap-hole towns like Riverton and Rawlins, Eastern Montana (or Montana reservation towns) and Idaho/Oregon Idaho/Washington border towns is much cheaper.
Riverton is my home town, I get to call it a crap hole. Rawlins is a prison town.
Sheep/Goat/Moose
Obviously Alaska is king. There is no comparison OTC tags for sheep, goat and moose.
Montana has the most goats. Quite a few moose and quite a few sheep.
Idaho has a lot of goats and moose.
Wyoming has very few goat tags and quite a few moose tags.
Alaska first, then it is all the same.
Elk
Wyoming has the fewest resident hunters (because of population) and is 90% the size of Idaho and 60% the size of Montana approximately. I think there is more elk available on a general in Montana than there is in Wyoming. Montana elk seasons favor bowhunters, Wyoming elk seasons are fairly fair to rifle hunters. I have not done the research on elk seasons in Idaho. I think it depends on if you are a bowhunter or not. I am not so I favor Wyoming. If you had horses and the equipment and were young enough to want to deal with brown bears in the Buffalo Thorofare there would not be any competition. But that is a tall order. Bowhunters would favor Montana.
Deer.
There are lots of very average to below average areas in Wyoming for deer. But there are a lot of deer.
Montana has a lot more whitetails, but I think you can get more tags in Wyoming.
Idaho has more whitetails than Wyoming does. I would split hairs and say Montana is slightly better, but it depends on what you like. I like hunting mule deer in the alpine. I also like sitting in a tree stand waiting for deer to come in. Alaska has Sitka blacktails, and you get to take 3 bucks, so for me it is the clear winner. I don't see any real advantage on the other three.
Pronghorns. Not even a close race. Wyoming, Montana then Idaho.
Extra credit:
Alaska has caribou, brown bears, wolverine and feral reindeer, woods bison (no tags yet, but coming soon) and muskox. So for the extra credit stuff Alaska is the clear winner.
There were mountain caribou in Idaho and Montana when I was a kid. I don't think there are anymore. Idaho does not have a hunt able population of bison on public land. So Idaho is clearly last.
The bison hunts in Wyoming and Montana are kind of a BS deal. But hey they have them so they are 2nd and 3rd in some order.
Women for the single man, or looking to become single man.
Alaska is probably not first, but it isn't last. I had very good luck as a single man in Barrow. You had your choice between the imported Phillipinas working as nurses in town, and a lot of professional women. There are about 85% as many women in Alaska as there are men, but the competition isn't as bad as people claim. There are so many completely feral dudes, borderline physcopaths that you'll have better luck than you think. There are also an abosolute mountain of chain-wallet lesbians in Anchorage. I had one cut me off when I was driving downtown on a Saturday, then end up next to me at a red light. she had her window down so I told her off, and she just turned into a marshmallow in the sun and melted bawling, is probably still crying her eyes out at that red-light today.
Quality of life (sports, bars, library, safety, security, crime).
Alaska has the worst crime, mostly native problems in villages and big city problems in Anchorage.
Wyoming has a lot of crime. Oilfield imported issues from out of state, and the reservation native problems.
Montana has the same, but not to the extent that Wyoming does.
Idaho has reservations too, but it is probably the safest.
Oilfield in Wyoming and Alaska had paid for a lot of infrastructure that doesn't exist in Montana and Idaho to the same degree. Libraries, parks, sports complexes, minor league sports, huge museums, and in the case of Alaska massive.
Wyoming has a couple small private universities, a few junior colleges and the U of WY has Laramie and Casper. Montana has a mountain of both private and public universities all over the state. I think Idaho has something similar.
Reservations are either really impactful like Riverton, or not an issue at all depending on how far they are away from where you live.
Wyoming is massively at risk for the Salt Lake and Denver bubbles to explode in population. Wyoming has always been someplace that didn't have the infrastructure of housing that could support a huge immigrant federal dumping situation that Omaha and Bowling Green got during the Kosovo war, or Afghan immigrant situation that Detroit and other areas have gotten recently. Saying that Wyoming is very close to the populations of Salt Lake and Denver. There is already a migration issue in Wyoming with retirees. Who are building infrastructure, and I think thee problems will come.
Alaska has a huge immigrant population from Asia and the Philippines. This doesn't seem to cause any problems.
Alaska also has fairly major military installations. The Air Force Bases in Wyoming, Montana and Idaho don't lead to the same form of retired and ex-mil migration that Alaska gets. Military wives are rarely happy about any of the WY, ID, MT locations.
Major cities:
Boise is 400,000 plus
Anchorage is 400,000 ish
Billings is 300,000 ish
Missoula, Idaho Falls, Couer D Lane, Bozeman, Fairbanks, Juneau, Casper are all around 60,000-110,000. Or in the case of Cour D Lane (no I don't know how to spell it), it is 30 miles from a 150,000 city in Washington.
That is my not-so deep dive on the subject.