30-06 and 7 mag are pretty close, just check the tables at 160-grain pill and 175 for 7 mag and 180 gr for the 30-06. You have a slight range advantage with a 7 mag.
The 300 win mag allows you to have an extra fifty yards of shooting range over the 30-06 at the most conservative estimates. Some will credit both magnums with more distance
The 338 Win Mag has about the same trajectory as a 30-06 for given bullet weights. It is more a bigger rifle than a faster rifle and it will do the same as an 06 with more effect on difficult shots.
With today’s premium bullets, the 30-06 will do just about as good a job as the 338 did in the 1960s and the 300 will shoot Elk at more distance.
I shot my first dozen Elk with a 30-06 and since used a 300 win mag almost exclusively, but it has only a range advantage.
All these, 30-06, 300 mag 7 mag and 338 mags work well on Elk, even the 270 and 280 will take Elk well with heavy well-constructed bullets. The 308 win does a good job at shorter range
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