I shoot P-dogs in Wyoming and use the .308. Hornady 110 gr V-Max for up to 300 yards and the Sierra 155 gr. Palma for distances out to 700 yards.
My longest hit so far is 647 yards (took 2 shots). The main reason for using
.308 is the variety of bullets and load data also LR ballistics are readily available.
I use the Tikka Master Sporter with a Leupold 6-24LR scope with target knobs. The rifle has a detachable five round magazine that makes it easy to switch from the short range bullet to the mid range one when a target presents itself.