Buy what ever you want for your 338/06, but most bullets in that caliber were built for the 338 mag. I have seen many elk shot with plain cup and core 338 mags and the elk die well. Please know I am talking from experience of 30 yrs of guiding elk hunters and seeing hundreds of elk die. I have been loading for the 338 mag and 338/06 for about the same time and have shot elk with both premium and so called regular bullets .. The results in either case have been elk in the freezer. Also, I like to shoot a lot, so expensive bullets are a waste on paper. So I shoot paper and kill elk with Sierras, Hornady's, Speer's and even Remington corelocks on occasion. I load for a good friend and neighbor that has a 338 mag using 225 hornadys at about 2800 fps. He shoots an elk ever year with one shot. I think that bullet would work fine in a 338/06 at a 150 fps slower. So again you buy what you want for your 338/06, but I know from experience premium bullets are unnecessary.
