I think the 308 is about the best all a round round you can own. It'll do everything an 06 will do in a short action.
Bullet weights all the way up to 180gr work.
The rifle in the picture is a custom Montana "Rifle Company left hand short action I had them make for me back on 03. I had them make it in 358 Win. Loved the round but found I didn't shoot it much because about the only ammo you could get were your reloads.
Last year I had it re-barrel to a 308, I didn't get it back till after deer season so this was the first year I could hunt with it.