Mountain;
This is anecdotal, but serves to illustrate the point. The year I took my pronghorn in to get mounted, the kid just ahead of me had a black bear he wanted skinned & the hide tanned. I asked him the usual set of questions about the gun & circumstances, and got a bit "wowed" over the answers.
He had been hunting antelope, just as I had been. His gun was a .22-250 where mine was a .30-06. He had a bear tag & just happened to see a smaller one running across a hillside about 200 yards from him & he decided to go for it. He made an extremely good shoot, offhand, IMHO. Put the bullet in the bear, running, just behind the shoulder & right at the bottom of the lungs. The bullet broke ribs on the far side of the chest cavity but did not exit the hide. Dead bear. Until you've actually experienced how fast a bear can move, most people don't believe it. OTOH, I didn't ask him if his life insurance premiums were paid up to date, but I do think he took a risk.
So, yes, any good deer rifle is perfectly adequate, but I don't consider the .22-250 to be good for that purpose. Myself, I'd stay with the .30-06 simply because I'm partial to the caliber.
900F