For a gun I hunt with, I favor a bright, clear, modest power scope (5 to 10 power max magnification) with lots of eye relief on a 338. I prefer a smallish objective (under 40mm) so the scope can be mounted low to the bore... quality glass needn't have a big "bell" to gather light well. Keeping the scope light and low reduces the "whip" it experiences under recoil, plus it's nicer to carry afield.
Leupold has some scopes in their VX-3HD and Mark 3HD lines which meet those standards without breaking the bank. They also have an excellent warranty that you will likely never need. If you can score an old made-in-USA Burris Signature with Posi-Lock, they are one of the most recoil-proof, repeatable, and clear scopes for the $$$.