I have found both the 308 and the 30/06 to be so delightful to shoot, reload, and obsess over that I have one of each caliber in two Ruger All Weather rifles set up with a Leupold Vari-X III 4 1/2X14 scope with "tuned" triggers. I enjoy them both, and could not pick one over the other to sell. The 308 is more accurate, but they are both game rifles. I like the controlled feed and the three position safety on a game rifle. These are bell ringers out to their maximum (for me) range of 300 yards.
My two precision thirty caliber rifles are 308's. A Remington M700 Varmint Special heavy barrel, and a Browning A Bolt II Varmint BOSS. Both have 24X Leupold benchrest scopes.
The Browning will outshoot the Remington, hands down. The Remington is no slouch. One must get past 300 yards to see the difference. The Browning has a Moyers trigger, the Remington has a carefully stroked factory trigger.
All four rifles have a 50 oz trigger pull with no creep. Fifty ounces is my preferred weight for most any rifle. This way, I have the same feel with any of my rifles, with the sole exception of my AR-15 Patrol Rifle.
If you want to see an obsessed person, you should see my rifle cartridge loading technique! LOL