Felt recoil will vary with weight of the rifle plus the style/design of the stock. If the rifles are identical the .338-06 will provide quite a bit more felt recoil than the .270 Win. - it is important to compare apples to apples.
By way of example comparing a 210gr Partition at 2700 to a 130gr @ 3100 in the .338/06 vs .270 Win respectively in an identical 8lb rifle, the .338/06 has 47% more recoil.
I do agree, however the 270 and 338-06 were identical rifles, 338 has a slightly heavier barrel, but 270 had a heavier scope. Even so the felt recoil was lighter in the 338-06.