To be honest, I really only use one rifle. For some reason, I'm most accurate with my savage 300 win mag when compared to my other large caliber weapons. I've yet to have any animal run off when shot by the 300. Everything I've taken has gone straight down when hit with the 300. Now, that's not to say that I couldn't make a poor shot and lose one, but it has yet to happen.
I guess I just am extremely confident that a well placed shot from the 300 win mag is a recipe for bringing game home.
In short, I would not feel outgunned hunting big bears with a 300 win mag, or any large game animal in NA for that matter. There are other calibers that could do the same thing, but the 300 win mag has my vote.