I have a 3-12x50 on my .340wby.

I have two 4.5-14x, one on a .300 win mag. another on a .270, just recently put a 4.5-14x44 on my .243win.

I really like 14x for those longer shots opposed to 10x, but I think any upper end mag of 10-14x would be a good set up on that .338. Personally on my .340 I wanted something with low power and high power, which tends to be hard to come by in afairly pricedscope IMO. 3-12 felt like a great compromise of both high and low powers, after all you can use that .338 for brown bear up close...or long range elk too.