338 is one of the great all round cartridges. If you handload you can pretty much tailor t to just about anything besides the really heavy game in Africa. My uncle has used one for years for elk back in my native CO and has taken it to Alaska a few times. Deer, elk, bear and moose have all taken a dirt nap from that rifle.
Personally I use a 375 H&H and a 9.3x62 but if I was looking to replace them the 338 Win would be on the short list of rounds I'd consider.