I talked to a nonresident hunter from Colorado this month paying $25,000 to a big game guide for a brown bear hunt on Kodiak Island. Met him at the air taxi service as we were preparing to fly out on a spring bear hunt of our own. This was his 4th AK brown bear hunt. He said $25K actually wasn't that bad compared to the going rates. This man was archery hunting.
Guessing another ~$3,000 in travel costs and gear.
Know guys that have killed them with 270 Win. I've killed them with 7mm Rem Mag. And of course .308 calibers have killed many. They will die with good bullet placement.
I prefer the .338 caliber. When all is said and done, the bear will be dead with good hits. The length of time from bullet impact till disabled and/or death is the difference.
If I was required to hunt with a guide, who would be expected to shoot any bear I shot that wasn't put down relatively quickly, I'd take a 338 WM on up. I'd want to shoot and kill my own bear, rather than having my guide kill it with his 375, after my first hit, or two.
Have shot several with the .338 Imperial Magnum and .338 Edge class cartridges. With good bullets, the bear don't stay on all fours for very long.