The .308 doesn't lose a lot of speed as the barrel gets shorter, (until you go below 16") but it does lose some. Decide if that matters.
Shorter barrels are handier in tight places, thick brush, getting in and out of vehicles in a hurry, and inside buildings. Something important to the military, less so for the rest of us.
Check you local hunting regulations. Some places have an 18" minimum barrel length, and so while a 16" is Federal legal to own, it might not be legal for hunting in your area. Most places it doesn't matter, but in some, it does.
Same goes for magazines. Some places have magazine limits for hunting, different than any limits for just ownership.
If you don't need (or have a use) for the rifle short for close quarter battle, the longer barrel gives a higher velocity.
The GI M14 had a 22" barrel, if I remember right.