A 7mm Rem. Mag with 150 grain bullet delivers 19.2 ft. lbs. of recoil. Your 270 Win, 16.5, a 30:06 with 180 grain bullet = 20.3 ft. lbs. I shoot a 165 grain SST in 7mm Rem. Mag with a recoil of 19.4 ft. lbs. of recoil. People seem to think when you see MAG your in for a nasty kick. If that MAG is a 375 H&H or 470 Nitro, yes, you better know how to shoot a big bore, but a 7mm Mag., you will have no problems.
http://www.chuckhawks.com/recoil_table.htm