All things being the same (rifle weight, stock design, etc...) the WSM will have slightly less recoil than the Win mag. This is due to the way that the cartridge burns its powder and the WSM has less powder to push down the bore behind the bullet. But, like BC said it is not all that much at all.

As far as on game performance goes there isn't any difference. If you reload or want to use heavier bullets than 180 grains the Win mag will have the advantage over the WSM.