My BAR is in .30-06 and is a great hunting rifle. I actually tried to buy the BAR in .308 but they were out of stock at the time and I needed a rifle quickly
(my deer rifle was stolen 2 days before the season opener while I was enroute by car to my hunting area).
That BAR is the softest shooting .30-06 I've ever handled. It wears a 1.75-5 variable power scope and is my preferred deer rifle for brushy areas. These rifles just "feel good" in the hand.
As far as caliber, choose whichever you prefer. There is little practical difference between the .308 and .30-06 unless you intend to hunt the largest game.
Matter of fact, if I were to buy a 2nd BAR, it would most likely be in .308 so my wife could comfortably use it. That's my story and I'm stickin' to it!