The 7mm Rem Mag is a belted magnum. That should give some indication (the .300 WM is a belted mag too).
I've owned multiple .308s and one 7mm mag (A Sako).
The 7mm is much stiffer in the recoil dept. However, I only have a "problem" with it when shooting prone. If I'm wearing a jacket or sweater, the recoil doesn't bother me at all. Of course I'm a recoil junkie, so "bother" is a relative term.
I've not shot a .300 WM, but understand the recoil to be more than the 7mm, which makes sense - it's a bigger bullet after all.
I have noticed that if my upper body is not in shape, the 7mm causes me to shake after a couple of boxes. The .308 never does this to me.
HTH,