I have the 308 and the 270 15'' barrels and my experiance is, the lighter the bullet, the lighter the recoil!
I use 150's in the 308 for big game but shoot a lot of 110 V max for fun and varmits. The recoil is noticeable off the bench. When shooting off cross sticks, recoil no longer seems to be a factor for me.
In the 270 I load a lot of 90 grain bullets but for hunting I use 130 grain Nosler balistic tip bullets.
I still want a 30-06 cause my dad left me a lot of ammo but the 308 is pretty good for almost everything I hunt. My 2 cents,
Lastchanc54