RE: New .308
I have been using a 308 Win. of one sort or another for probably 30 years now here in SE Alabama. I started out with a Winchester Model 88 and after it was stolen went to a BAR. Several years ago I bought a Ruger Mod. 77 and now use a Styer Pro Hunter "Mountain". Don't sweat the ability of this round. I took a fine , heavy mule deer in Eastern Montana at a ranged 335 +/-. Hit him nearly perfect behind the shoulder and he went maybe 50 yards. I have no clue what it weighed, but the folks I was hunting with were locals and told me that it was a "toad" ... their expression for a bigger than average deer. I am guessing 325# +/-.
I have killed many, many deer and hogs with the 308 Win. Mpst in the 100-200 range. I dropped a rather large feral boar in a swamp just south of Montgomery in '87. It weighed about 415# field dressed. The guy that processed it charges by the pound, field dressed. His scales were not "certified" but I'm guessing this is close. This boar was hit broadside at about 80 yards and ran maybe 30 yards. So the round will do the trick on bigger stuff if placed well.
The answer to your question, in my opinion, will be the hunting ammo that groups the best. Like mentioned before my comments, anything 150 gr. up will do the trick. I would offer that the 165 gr. is about the optimum bullet weight. I don;t care for 180 gr. or heavier. Takes up too much case space.
As far as bullet type, any of the "hunting" bullets will do. My brother has never used anything other than factory stuff in his 308, Winchester Power Points. I hand load. Personally I like either Nosler Partitioned or Speer Game Kings. Partitions are "tougher" than the Game King. The game King is a boat-tailed bullet and excellent for longer range accuracy. These are "old" school bullets .. but so am I (old school), however I am looking forward to trying some of the "new" bonded bullets in the hand loads for my rifle.