Your '06 is plenty powerful for anything you state above. The 338 isn't fun to practice with, you'll develop a flinch and be less accurate.
Shot placement is the key. Mule deer at 400 yards.... well my little 7mm-08 will do that. I won't because I like stalking to less than 200 yards. No trees here in SW ND so no cover isn't a valid reason for a cannon.
Save the cannon for dangerous game like a bear.
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