I would pick the .338 because in practical terms .300 magnum offers nothing over .30-06. Extra recoil and blast are not practical.
You sir, are delusional. Offers nothing ? Just in Hornady American Whitetail 180gr, the 300 is nearly 300 fps flatter and almost 2 inches flatter at 300 yards. You should get out and actually EXPERIENCE some things, as the other guy said. An animal wont know the difference until you get over 800 yards, but the ease of less holdover is what the 300 Win Mag was intended for. Besides, the 30-06 needs to be retired, I'd take a .308 or .30 TC over the Ot Sux any day.
