all of your mentioned calibers will take down white tail no problem with proper shot placement. All of your mentioned calibers will shoot paper at 700 with practice, a good rifle and quality ammo. In SD we have BIG DEER, not just nice racks, but BIG DEER. My recent 3x3 weighed in a 220lbs field dressed and headless when I dropped him off at the locker. A .243WSSM and 75gr VMAX dropped him in his tracks at 397m, the doe took a similar hit and wobbled about 20m before passing out from blood loss. The antelope i got in Oct was taken at 683m with the same ammo and same results.
absolutely nothing wrong with the .308 or the 270 or 260...anything from .30 to .243 for that matter. just get to know what your weapon likes, and practice. I will admit, i was nervous about using a 75gr 243 bullet, my dad uses 150gr 7mm and my cousin uses 175gr 308, and we all have had the occasional deer run a hundred yards after a good shot, deer are tough.