Recoil from a 300 Weatherby is fast and sharp. It's like getting punched in the jaw. Although there is unquestionably more recoil from a 458 Winchester, I actually prefer to shoot it because while the recoil is large, it's slow enough that you can sort of roll with it. Not so the Weatherby.
That said it's a formidable round, powerful and flat shooting. It would be great for elk, moose and similar. Ammo is expensive and premium bullets are a must. If the game gets really big, I'd personally prefer to trade some of that velocity for a bit more frontal area and bullet weight, but that's JMHO.