I don't know if you hand load, but that may be the answer.
I started shooting a Savage Striker, in .308 Win, a few years
ago, to get around a shotgun/muzzleloader/handgun only
hunting zone. I can shoot a handgun, with a rifle chamber,
but I can't shoot a rifle??? Anyway, I developed a 130 gr.
Barnes XBT load, driven by W748, that chrony's at 2775 fps,
out of my 14" barrel, and it really hammers northern Whitetails.
I have yet to recover a bullet, and the last deer was quartering
towards me. The bullet hit center low, in the front shoulder,
blew up some bones, turned the vitals to blood pudding,
and exited through a rib, on the far side. It was a pretty
dramatic "Bang Flop"... or more like a "Bang Flip". I
have had nothing but DRT results with this load. Well one
stumbled 50' before falling, but by judging from the damage,
it was a tribute to the toughness of whitetail deer. It was DRT,
but the critter's brain didn't know it.
I shoot some 150 gr. Hornady Soft Point bullet loads, out
of my BAR, in .308 Win, that chrony about 2850 fps, and
it puts deer down, with authority, too. I don't think the
problem is with the .308 Win. chambering. It is plenty capable
of dispatching large deer. I would be looking hard at ammo,
or shot placement, if results were less than expected.
Squeeze
P.S. I have .30-06 Sprg, and 300 WSM, rifles, too, and I have
never been able to tell the difference in these over the .308 Win,
in deer shooting. They burn more powder, and they thump me
harder, but by my experiences, they don't kill deer any better
than the .308 Win.