The 223 M16 variant which marine snipers use with a 1/8 twist and 80 grain bullets is more than enough to kill anything short of elk and bears at normal ranges. My choice for a modern military rifle would likely favor the 6.5 Grendel cartridge over the 308. The Grendel is big enough to kill nearly anything, is still supersonic at 1200 yards, and is supremely accurate. 308 Bullets on the other hand have to be 165 grains before they can get to 1000 yards and still be supersonic. The standard 147 gr NATO stuff won't cut it.
My father inaw has a WWII Italian Carcano 7.35 mm and he asked me to do some research. Turns out it was a replacement for the 6.5 mm which the Italians decided wasn't a very good very good cartridge back then and the Italians tried to switch over to the larger caliber before the war but couldn't. Nice gun though. Someone was using it for shooting sharks off a fishing boat before he picked it up.