I have followed this thread, not because I have any experience or any chance of ever hunting a Brown bear, but because I once did dreamed about it and wanted to see what experienced brown bear hunters said.
Years ago I thought I could affort to take my son to cape buffalo and and Brown bear hunts. We studied, talked to guides and other hunters and got two M70 CRF 375 H&H topped with 1.5-5 Leupold on QD rings and kept iron sights. We developed loads and practiced. Them 375 H&H push hard, not kick, but push. Then life happened. We did managed a SA hunt, but plains game. Now we just like to read the stories of others, no way I can afford to pay for a brown bear hunt.
Anyways, most of the guides we talked to, said, pick a 30 cal or larger rifle you can put three rounds on target in short time.
Personally, I would not take anything less than a 338WM, and I have heard the stories of the Eskimo woman using a 223.
I am just reading, and and enjoying the opinions.