I've used the .338WM as my 'go-to' rifle since 1992.
I consider the .338WM about perfect, for hiking around in grizzly-moose country.
I've shot moose, black bear, whitetails with it. I've seen spectacular kills, and other times I've seen animals 'soak up a few' before toppling over. But I have seen those same type of reactions with pretty much any other cartridge, bigger and smaller.
If you hit any North American big game animal, in the right place, you're gonna kill it. Just some will kill quicker.
As far as bullet selection, I've never had an issue; 225gr Nosler Partitions have been my favorite. I've also used 250gr Parts and 250gr Hornady Interlocks, and those are both excellent; in fact dollar-for-dollar, I consider the 250gr Hornady Interlock as about the best combination of price and performance.
Edit to add: I have 2 .338WMs: I have a 'working rifle'; a M700 in a Wildcat Composite stock. Scoped with a 1.5-6x Baush & Lomb Balvar scope. The other is a M70 Supergrade; pretty thing... wears a Leupold VX3 1.75-6x scope.