I have a Win Model 70 EW 338WM, a Kimber 8400 Select and a Kimber Super America. The 338WM is definitely a viable cartridge. Good to 800 or so.
For normal shooting ranges, even out to 500, a conventional bullet like a 225gr Partition or Accubond on deer or elk is perfect, you can step it up to a 250 for either too, and this will also work on bears.
No reason to second guess, it just works.
If you want to shoot ELR, like me, you can go 338-416 Rigby Improved like I did, or 33CX, 33 Nosler, 33 Norma Mag or Lapua.
But they are a niche' class of cartridges that resemble tactical type shooting and the rigs that go with them. Of course you can hunt with any of them, but recoil goes up with them as speed increases.
Cheers.