Re: pick one and tell me why
338 Win Mag, hands down.
More versatile, more availability of factory ammo, much wider selection of bullets of various weights and construction, and much more manageable to shoot. The 8mm Rem Mag was the nastiest recoiling thing I've ever shot, whereas the 338 is able to be controlled with a little bit of practice and trigger time.
I'll never own another 8mm Rem Mag, but would have no qualms about owning another 338 Win Mag if I was in the market for something in that category.