On the same token, I was reading about Craig Boddington's article about his last Alaskan brown bear hunt where he killed a bear with a single shot from a 338 WM. I forget what the distance was though.
After doing research on brown bear hunting, I don't know what gun to recomend, but the 338 WM is currently the smallest suggested round by many outfitters. It's smaller, but hits harder than your other traditional calibers. Opinions on the best brown bear caliber are nowhere near as contentious as the best whitetail caliber though.
Good luck on your hunt. Shoot straight, and don't stand in front of your guide just in case things go bad.