Your question is really easy for me. I could select my 300 Win Mag in a Browning Safari (Belgian), or one of the Weatherbys. The 7mm Wby MKV comes immediately to mind. They are both very accurate and have that little bit of punch that the 308 class of rifles seems to lack. Bullet selection is something to think about.
For those concerned about these rifles lacking the "big bear" stopping power, I guess you have to work with what works for you. I realize the 458 I seldom shoot would work well for the bears, but little else on this continent. And the handling characteristics of that heavy rifle do not impress me as something I would want to carry all day on a hunt.
Larry