As I'm reading this I think you're asking for a 308 target bullet that would work for hunting as well.
I'm also assuming you don't reload.
This leads me to recommend Hornady Ammo.
In the 308, Hornady mates the A Max in 168. This is a target bullet and according to Hornady and I agree, is not a hunting bullet.
Hornady also makes the 165 Grn SST, which has nearly the same BC as the A-Max, its supper accurate and is a hunting bullet.
I personally think the SST is a great deer/antelope round BUT some times the jacket may seperate on heavy game such as Elk.
Soooo...................Hornady came out with the Interbond. This is basicly the same as the SST, but the jacket is bonded to the core making it a better Elks size hunting round.
Hornady, besides selling the bullets, sells loaded ammo with the SST and IB Bullets.
Again they in my opinion are as accurate as the A-Max.
Personally I don't use the 308 for hunting thought I do use them in a couple of my target rifles. I've shot the SSTs in my target 308s and they seem to work as well as the A-Max.
I hunt with a 270 Winchester. I use 150 SSTs for practice and 150 IBs for hunting. I load them the same. (The SSTs are cheaper then the IBs). Using the same powder/charge, same brass and primers they shoot the same place, at the same velocity. I don't have to change my sights when I switch from SSTs to IBs. I just shoot more SSTs because they are cheaper.
So if I was to recommend a bullet that works for both hunting and target I'd pick the SST. It will work on deer and antelope but I'd chose the same load using the IBs for elk.
Hornady sells both loaded ammo and bullets using the SST and IBs. I'd recommend the 165 grn SST/IBs for the 308.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071