I would recommend Federal Vital-Shok 165gr Trophy Copper for your .308 Win. I shot a mule deer in 2015 at 341 yards using that ammunition and punched a hole through the heart. Here's how it shoots from the rifle I used for that hunt. Federal offers a 150gr version too but I haven't tried that load. As for Barnes, I work up loads for all my hunting rifles using Barnes TTSX bullets. I like the 165gr bullets in my Kimber 84M Montana (.308 Win) with 5-shot groups typically in the .75" range or better. I show a target
here.
Here's a 3-shot group using the Federal Vital-Shok 165gr Trophy Copper load ...
... and a 5-shot group with the same load.
Here are some expanded 165gr TC bullets from the sand berm behind my target.