You'd need some kind of scale to tell the difference. A 308win runs a heavier pill, but less powder charge, and comes in a lighter short action rifle. The 270 runs a bit lighter pill a lot faster, with a bigger powder charge, but in about a half pound heavier action. It all comes out in the wash.
My personal 140grn 270 and 165grn 308win loads come up to 14.95 and 15.33 ft.lbs. of recoil energy, respectively. The day my shoulder is sensitive enough to feel that difference, well, that'll be the day...