I own both. I've recently discovered my .308 will launch a 125gr bullet at 3100fps - pretty much duplicating the.270 to 400yd.
Not only is .308 a short action, but it utilizes barrel length more efficiently than a .270. My .308 has an 18.5" barrel. I don't think the .270 is suited to any less than 24".
Beyond 400yd, the .270 has the edge. However, with a standard 1:10 twist it struggles to stabilize bullets with a G1 over ~.525... at that point you might as well go .280 or .260 or something in the 6.5mm or 7mm family.
Right between the .308 and .270 is the 7x57. Goldilocks, though all are good choices.