Several years ago the Alaskan Fish and Game did some testing of different cartridges to be able to advise hunters and fishermen about what to carry for brown bear protection. They concluded that the magnum cartridges 375 and up performed best. But the 300 WM and 30-06 when loaded with 200-220 gr bullets tied and were pretty close behind 375 mag. Lighter 180 gr bullets didn't provide the necessary penetration for the big bears.
While the 375 looked slightly better on paper, and would certainly be a good choice, they recommended 30-06 for most people due to less recoil and more common rifles. The 300 WM was acceptable, but they ranked 30-06 above 300 WM only because the extra speed of the magnum offered no advantage and they felt the added recoil was a negative.
Interestingly they found that the 30-06 or 300 WM loaded with 220 gr bullets out performed rounds such as 338 WM, 35 Whelen, 45-70 and slugs from a 12 ga shotgun. Finn Aagaard, an African guide and gun writer came to the same conclusions for shooting the larger game in Africa.
Making a trip to Alaska is a bucket list item for me, but I'll never hunt there unless I win it big in the lottery. But If I did I'd feel just fine with a 300 WM or even my 30-06 with the right bullets in the chamber.