I shoot a 300 WM plenty. I've taken two shots with an 7mm STW that was enough for me. It has a lot of felt recoil. The gun that I was shooting was a Rem 700.
As someone that has owned three 7mmstw rifles,I find the recoil about equal to the 300winmag.The 7mmstw is a great long range hunting cartridge but the barrel life will be shorter than for the 300 win mag,so it won't last as long as a target gun.
I have him beat a little bit on trajectory, but he can use up to a 200 gr bullet in a 300. 7mm only goes up to 175. It's all in what you want.
I have taken pronghorn,deer,bighorn,elk and moose all with 140gr bullets out of my 7mmstws.If you choose the right bullet,you don't need a heavier bullet.