I've discussed polar bears with a few natives in Alaska and also in the NW Territories. One in the NWT guides for them and has supposedly been in on around 100 polar bear kills. They all seem to prefer mild mannered rounds of .257" or 6.5mm. The NWT guide recommends the .243 Win to his clients. They all say that .300 Magnums (I presume they're referring to the Winchester round) is too destructive. I am not sure if they'r referring to the hide, the meat or both.

I am guessing they shoot their bears bayed up by dogs or those chased down on snow machines, so close shots are the norm...but that is just a guess. Take that for what it is worth...