I'd lean towards the 300 win mag as you have a bit more versatility and a bit less recoil. All things equal, the 338 is going to have more kick. I seem to remember a calculator on the internet where you could measure the amount of recoil for a particular load...
The 300 gives you more opportunity to shoot a bit light, higher velocity loads. based on what you already have in your arsenal I'd say it would fit the bill. Plus, if you do a combo deer/elk hunt, you won't get razzed for shooting a whitetail doe with a 338!
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