Assuming accuracy is equal, which may or may not be true, I'd go with the more rugged bullet. Of your choices I don't know which that is. I'm of the opinion that the 243 is light for deer unless the bullet is meant for deer. That means a bullet constructed not to fragment into pieces.
Premium bullets are not needed for deer, so if a "green-box special" gives good performance on deer and they shoot fine, so much the better.