Both are good choices, both originate from the 458 Win case as does the 264.
Don't be so worried over recoil, it's like riding a horse, you either go with it or get bounced around. Rifle weight and balance as well as stock design are very important factors. You want a stock with limited drop, correct length and a wide butt. If the stock fits you and the buttplate is wide and long it'll spread the recoil energy over a larger area.
My favorite stock is the NRA stock design found on pre-64 M70's. Other rifles have these as well.
Another secret to dealing with recoil is learning to sqeeze the trigger rather than jerking back on it. Yanking on the trigger is one of the best ways to master the perfect flinch.The more you flinch, the more you feel the recoil and the more the recoil, the more the flinch , and so on ------------
With equal rifles the recoil would be more with the 338 as the bullet is usually heavier creating more resisitance, giving you more recoil. Ammo is a bit cheaper for the 300 win as well. Why not eventually buy both. That's what I do.
Rod