I've personally always enjoyed reading what the professionals have to say about all-round cartridges. Craig Boddington wrote two books;
American Hunting Rifles & Safari Rifles
In the back of both of these books Craig surveyed Guides & PHs.
American Hunting Rifles: top three Choices for All-round use:
1).300 Win Mag, 21
2)7mm Rem Mag, 16
3)30-06, 16
But if you look at the guides recommendations to clients which covers deer, elk, moose, sheep, goats, & bears - top three:
1)7mm Rem Mag, 88
2).270 Win, 81
3)30-06, 58

Safari Rifles PHs' All-round personal choices top 3:
1)375H&H, 81
2).416, 7
3)30-06, 6
Recommendation to clients; one rifle safari
1)375H&H, 70
2)30-06, 8
3)300 mag, 5
Two rifle safari and drop the big rifle which is the 375H&H top three:
1)7mm mag, 19
2)300 mag, 18
3)30-06, 13

Based on those recommendations from the "Professionals" if you never plan to hunt dangerous game and you want an all around do it all rifle cartridge then buy a 7mm Remington Mag, the clear professionals choice. But if you plan to chase stuff that bites, stomps, or gores the clear Hype of the 375H&H would be your choice.