YES..but "significantly" is a relative term..I do believe in having young shooters starting with very mild to mild recoiling calibers..the .257W to most is not mild recoiling..it is severely over bore..

Per this chart, the recoil difference between the two is between 60 to 70% more for the Weatherby..
http://www.chuckhawks.com/recoil_table.htm

As I am assuming your son will not be taking shots past 300 yards or more.. I would stick with the Roberts..its a really cool old classic cartridge with plenty of energy to kill most anything here in N America..

Ripp