Ya can't kill 'em too dead, so there is nothng wrong with the .338. Definitely don't need all that horsepower for whitetails, though. Don't even need a 30-06 for whitetails.
If you take an occasional longer shot, why not a 260 Rem or a 7mm-08? Do you handload? If you hunt thickets and timber, why not a 260 Rem or 7mm-08?