Depends on the weight of the gun, the stock design, recoil pad installed, and a few other things.

My 300WSM I built a couple years ago hurts less than my .270 Winchester. But the 300 has a stock I built to fit me, it weighs in at about 9 pounds and has a decelerator pad installed. My .270 Winchester has the original stock on it (which is too short for me), weighs about the same but has a plastic but plate on it.

When the WSM's first came out they were all chambered in light quick handling "mountain" type rifles that weighed about 6 pounds. Now there are more and more "standard" weight and "heavy" weight rifles that are chambered for the 300 wsm that will weigh within a couple ounces of a rifle chambered for the 300 Win mag. So yes if you compare the same rifle the WSM will kick less.