There is no way of resolving this as it will all be based on anecdotal evidence. One guide I hunted with said the .338 just thumped Elk harder but his personal rifle was a 300WM.

I think you would need to shoot upwards of a 1,000 Elk to come up with anything meaningful and perhaps even not then. Elmer Keith used the 30-06 with FMJ military bullets with the nose filed off and decided it was no good on Elk, no wonder I wouldn't even use that combo for squirrels. In his case due to lack of good bullets the 33 bore was a superior choice. With today's really incredibly good bullets you can drop down in caliber quite a bit. Idle speculation but I would venture that a 7mm mag. with today's projectiles would far exceed anything Elmer had at the time.

"When you disarm the people, you commence to offend them and show that you distrust them either through cowardice or lack of confidence, and both of these opinions generate hatred." Niccolo Machiavelli