I can not address the .338 as I don't have one. During the season (white tail) I tend to use witch ever one of my rifles appeals to me that day.
The low power end is a 30-30 Trapper,the top end is a .375 H&H,as I load each for the job at hand I can see no problem with the big gun. Actually I see less loss of eating meat with the .375 than I see with the more traditional deer cartridges ( .25-06, .264, .270, 30-06 .308, or .300 WM.)
All said if a .338 blows your skirt up that's what you should use( with proper loads)