If the rifle is a deer only proposition then you can't go wrong with a 243 Win. Less recoil and enough bullet to get the job done if you are using good 100 grainers. Even better with a minimal increase in recoil would be a 260 Rem. Better still would be a 7mm-08 Rem and that will do anything a 308 Win will do with less recoil.

BTW, the only 308 Win I ever saw that had more recoil than a 270 Win was a Remington Mohawk 600. It is so small and light that it is not fun to shoot off the bench all day. Full size 308 Win rifle is much milder than almost any 270 Win rifle, unless you are shooting 90 grain bullets from the 270 and 180s from the 308.