RE: 308 for moose
bigbulls - You might want to consider getting your boy a .260 Rem, 6.5x55mm Swede or a 7x57mm Mauser. All will kill elk without a problem, all have minimal recoil and all make excellent " grown up" cartridges, too.
By the way, I share your love for the .338-06. My next rifle will also be chambered for that cartridge.