The .308 was pretty stout in the recoil department before I changed the recoil pad to a limbsaver. Now I can goto the range and shoot all day.
My .308 barrel has not yet met a heavier round that I can get a decent group out of... 180gr ~ 4" group. With some el-cheapo 150 gr wolf ammo, I've gotten 0.75" groups. I'm hoping that some of the 165 gr stuff will have some more reliable groups, but still have a little more bullet mass.
I've not had a gun before t hat was actually sensitive to the type of ammo I've put through it. It definitely has the potential though.
Ultimately I like the .308 because it's less expensive to plink with... but my understanding is both those rounds are good for your stated purpose.