Copied this from Alaskan Department of Fish and Game.

Big Magnums Not Needed

The rifle you bring hunting should be one with which you are comfortable. Because of the presence of brown and grizzly bears, many hunters have been convinced that a .300, .338, .375, or .416 magnum is needed for personal protection and to take large Alaska game. This is simply not true. The recoil and noise of these large cartridges is unpleasant at best and plainly painful to many shooters. It is very difficult to concentrate on shot placement when your brain and body remembers the unpleasant recoil and noise which occurs when you pull the trigger on one of the big magnums.

The two most common complaints of professional Alaska guides are hunters who are not in good physical condition and hunters who cannot accurately shoot their rifles. Because these hunters do not practice enough they cannot shoot accurately enough. They miss their best chance at taking their dream animal or worse yet, they wound and lose an animal. Most experienced guides prefer that a hunter come to camp with a .270 or .30-06 rifle they can shoot well rather than a shiny new magnum that has been fired just enough to get sighted-in. If you are going to hunt brown bear on the Alaska Peninsula or Kodiak Island, a .30-06 loaded with 200- or 220-grain Nosler® or similar premium bullet will do the job with good shot placement. Only consider using a .300, .338 or larger magnum if you can shoot it as well as you can the .30-06.