Well I've been target rifle shooting for those fifteen years that you've been away, firing about 20,000 rounds in that time from my .308 target rifle. Which weighs about twice as much as a hunting rifle (so its recoil is only half that of a hunting rifle); and it has a recoil pad; and I shoot it with a sling and heavy leather shooting jacket that includes a good thick shoulder pad. And to this day, I must still constantly fight away a tendency to flinch and produce a poor shot....! It's not that the rifle hurts me when I fire it; it's that it is such a huge, startling event, that a poor shooter's brain quite reasonably decides to try to "get away from what's about to happen". Result: a flinch, that oftentimes ruins an otherwise good shot delivery. Even though I've fired *much* bigger rifles, without getting hurt, it still takes a huge amount of mental concentration and discipline for me to produce a trigger break on my .308W target rifle that is as good as that which I can produce while dry-firing.
(guess that's a *LONG* way to say that there's no need to hate to admit that you're "somewhat sensitive" to a .308's recoil).
X2