Does anyone here on the campfire feel a difference in recoil between shooting a 270 Winchester loaded with a 150 grain bullet and a .30/06 using the same weight bullet?
No, but yours is an apples/oranges comparison. A 270 150 is in a different class of bullet than a 30 cal 150 of lead core construction.
A more accurate comparison (BC/SD) is the 270/150 vs 30-06/180... I definitely can feel that difference in equal rifles.