I can only assume that you're considering this caliber change because of a shot out barrel or some other problem. From all I've heard, the .308 is great for most game in North America and few people are disappointed in it's performance.
With regard to your desire to consider the .260 Remington, I think you'll be very happy with this caliber if used for the hunting you mentioned. I hunt in southwest Alabama and I've had fantastic results on whitetail using 120gr. Ballistic Tips from 80-200 yds. and I love the flat shooting characteristics of the round. Never had a deer take more than 3 steps after being hit so don't let people tell you that the .260 "ain't enough gun".
Best of luck with your choice & safe hunting to you.