I would bring the 338 and be done with. No sense taking two guns, especially when the trajectories are so similar.
As for the scope, a 1.5-5 or 6, 2-7, 2.5-8x would be fine for the most part. If it were me, I'd go with the Leupold 1.75-6x VX-III. It's a really nice scope, light, and rugged.