You really are talking apples and oranges, or chalk and cheese as they say here..A better comparison would be the 300 Win Mag/7 Rem Mag or 308 Win/7 x 57 Mauser..
The accolades of the 7mm is a good choice of bullets, good velocities for long distance, doesn't leave you for want..the cons are that it is a barrel burning round, is an overbore cartridge which is not very efficient in hunting length barrels.
The .308 also includes a vast choice of bullets, velocity is ok but not stellar, accurate up to 800 yds, very stable, and it will shoot for many many years, not a barrel burner, cheap easy to find components, and lots of ballistic data...cons are it doesn't pack the punch of the larger 'magnum' 30 cal class..
I wouldn't hesitate to take either into the field, after any large north american game..Whatever you shoot, hit the range as much as you possibly can, know the rifle and where the bullet is going to strike..Shot placement is the name of the game...
JR