I also shoot the .308. If I was stranded on a desert island with large game and could only pick one ammo to use . . . thought I had an answer didn't you?!!
Definitely go with premium ammo. Winchester only comes in 150 grain in 2 ammo's.
So I'd have to say go with Federal Premium P308E for medium range (under 200 yards). It is loaded with 180 gr Nosler Partition. If you're going to be shooting farther than that, then go with the Fed Pre. P308H. That is a 165 gr Barnes Triple Shock. It will give you better accuracy at farther distances. Either round will do the trick.
If you can, get both and take them to the range and see what your gun likes. And practice long shots!