RE: 300WSM or 338 Win Mag for CO Hunting???
Recoil will be an issue in the Tikka rifle. It is light, and the stock design seems conducive to a sharper jolt than others. I've shot one in .270 Win that was noticeably heavier in the recoil department than the Weatherby Vanguard in .270 Wby Mag and Ruger M77 in 7mm Rem Mag we had on the same bench....and these are more powerful cartridges. I know I wouldn't want to shoot a Tikka in anything much bigger than .270.
You really don't need a big .338 Win Mag to kill elk. If you want one, that's fine. But getting a rifle that is more comfortable to shoot, such as a .270, .280, .308, .30-'06 or 7mm mag, means you'll shoot it more often. That alone will make these smaller rifles better elk killers for you at longer ranges than the big boomers that will only get a few rounds put through them every now & then.