Substantial!
I own a 300wby, and a 270wsm and its a night and day difference. Ive shot the 300wsm and will own one someday. The 300wsm recoil(to me) is very simmilar to my 270wsm.
Just a thought, if your looking to purchase one or the other look into the 300RUM. You will gain (if ever so slightly) over the 300wby, and you dont have to mess with a belted case. All that being said, if I were to pick an all round performer(for north American big game) that wasnt overly expensive to shoot Id go with a 300wsm for my all round hunting rifle.