Moose and elk anywhere, your .308 with Barnes TTSX ammunition will take care of them no problem. I'm from B.C., and know of plenty of large northern moose taken efficiently with a .308. Now if you're talking about the big bears, I'd want a minimum of a .338Win Mag, firing solid copper bullets like the Barnes, or a .375, either Ruger or H&H.
The only slight advantage to the .338WM is cost per round versus the .375, and that if
you lose your ammo you can find .338WM in most village general stores up there. I'd be inclined to go with the .375 Holland & Holland if I were hunting big bears.