+1 What Art said.
A 308 can drop pretty much anything on the North American continent, with a decent shot.
338 Lapua may have some advantages, particularly at longer ranges, but if you're price sensitive to ammo, check out cost per round before committing.
If you want to engage polar bears, big African game, or vehicles particularly over 1000 yards, there's always the .50. But a .308 is pretty blasted solid.
أنا لست ارهابيا
.50 BMG: 1 Shot 1 THRILL!