The only right answer is that there is no right or wrong answer. With the proper ammo and shot placement, it won't make any difference at all on deer inside 100 yards or even out to your max safe shooting range. Neither are hard kicking rounds and both are now very common/easy to find (.308 obviously being on every shelf on the planet with the Creed catching up due to the popularity). Can't go wrong with either of them.

One other caliber to throw into the mix - 7mm-08. That may be the goldilocks of the two you're comparing and the best of both worlds?