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338 Federal is based on a 308 Win. case and has considerably less powder capacity than the other two. What do you consider "some distance shot," and what do you plan on using your rifle for?
I had a weatherby 338-06 ultra light and it would push a 185 gr.triple shock to 2925fps and a 210 Nosler to 2830 fps.It will do anything the other magnums will do with less recoil,no animal will know if it was hit with a mag or the 338-06.
just my 2 cents.
Then you want the 338 win if you want something closer to the 338 lapua at least from what you have selected there. 338 Remington Ultra mag would be closer yet.