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.

My big game rifle is a 325 WSM, It has the lower recoil like a 300 win mag but the 338 knock down. Plus Browning is a big pusher of the WSM cartridge so that was my excuse to buy a pretty xbolt which btw shoots like a dream, has the best feeling action i've felt, a great recoil pad, and when reloaded with berger VLD's shoot extremely tight.

I no factory ammo is a little expensive but like most this isn't a gun you go plink and play with.. but i would buy this gun a million times i love it.

Nothing wrong with the .325wsm, it's basically interchangeable with the .338wm.
I wouldn't feel undergunned with that if I ran into a grizzly, but if I were hunting
them on purpose I'd go with the biggest calibre I know I can shoot accurately,
and that's the .375.