Although I've never hunted browns ($$$$), I've taken 3, black bear. All were perfect hits, at less than 60 yards, and all three ran off, 50-75 yards.
The last one was taken with a .458 Winchester mag. RIFLE. It was a broadside shot at less than 50 yards. Perfect hit, just behind the shoulder. It took out lungs and heart, but, the bugger still ran about 50 yards, before he expired! Just glad all of them went the OTHER way, instead of trying to eat me!
I finally got to take a wild boar with my .454 Ruger Super Redhawk, yesterday. The 1st shot was less than 25 yards, broadside. I put the 265 grain Swift A-Frame, right behind his shoulder. Although it knocked it down, the bugger got back up again, and when it turned, I BROKE the other shoulder. The bugger still didn't know he was dead, and got up again! I couldn't believe that it could even move, after breaking the shoulder, so, I pumped a couple more in it, and it FINALLY stayed down.
I've hunted in Africa, and always took shoulder shots, when possible, and it has always dropped them like a rock.
Although I prefer to hunt with a handgun, if I was going after a brown, I think I would like to have SEVERAL people with BIG guns backing me up!
Good Luck on your hunt!!