I don't mean to spoil the party, but in factory loaded ammo, the .308 Winchester is the superior round and will put game down faster than the 7 Mauser. If you hand load the 7 Mauser, then it will be perhaps the equal of, but not better than, the factory loaded .308 Winchester. As a practical matter, you will not see a hair's worth of difference in terms of their performance on game.
Also remember, you can buy the .308 in factory loaded Hi-Energy or Light Magnum loads, which propel the 180 nosler partition bullet at the same velocity and energy as a regular 30-06 factory load.
All this having been said, the 7 Mauser is still a great cartridge.
Best Regards,
Big Paulie,