The 7mm-08 Rem with out penetrate a 308 Win and carry more downrange energy.
If you compare the .308 shooting 180gr. nosler partitions to a 7mm08 shooting 150gr partitions the .308 has over 200 lbs more energy at 300 yds. Not saying the 7mm can't do it but the .308 will hit harder. Up here in Ontario the .308 is an extremely popular round for moose which can hit 1000 lbs on the hoof so in my opinion that qualifies the .308 for pretty well anything short of dangerous game.