Sorry, but it is possible, the WSM uses less powder to do the job. Less powder, less recoil. I fear you are a victim of "back in my day" syndrome. The WSM cartridges are superior to their long action counterparts in every way, not by as much as some may think, but more than people locked into "old school" thinking will admit.
Now that that is over with... the difference between the two, in actual use, assuming the
rifles weight is the same, will be barely noticeable to most shooters.
And at any rate..... I would still use a .308, I was trying to make a point about overkill with the Flak jacket comment in my previous post .... very few game animals in Canada wear them.
This is from Chuck Hawk's rifle recoil table... so you don't have to take my word for it...
As you can see the slightly
faster WSM cartridge, even in a
lighter rifle, has
less recoil