For all of the ethics concerns of taking game at 600 yds... the OP asking the question is on the complete opposite side of the world that we're on. We don't know his ability, we don't know his situation, and we don't know his purpose.
War may be talking about protecting crops, or protecting other things. While I certainly agree with everyone who has chimed in on ethical shooting, you have to really think about the application. I know men that I would trust and not question taking shots @ 600 yards... and I DO believe in being as ethical and humane as possible. There are alot of people that shouldn't be shooting beyond 100.
With that, the 7mm rem mag is in every way superior at this range. A flatter trajectory definately helps at that range as you're getting into a healthy bullet drop just by being off in range estimation by 50 yards. It's also the very clear winner in energy delivery. .308 starts to peter out pretty quick beyond the range in question.