Shot placement is what kills the animal, not the caliber nor the amount of powder it's got behind it...
1,200 FPS in 150 grain bullet out of a 30/30 will drop an elk, just like a 300 grain slug traveling 2500 fps out of a 460 Weatherby Mag. But the Weatherby will take out more meat on the way through.......
Shot placement is paramount. If you can't shoot it where you want to shoot it then do what many do and get a bigger gun.
I personally think that 308 you have is a great hunting weapon.
I am to opinionated today....