Concerning these two cartridges, without getting into the math of the calculated recoil, having the same felt recoil or not is almost entirely subjective to the fit of the rifle to the shooter. I've had 308's kick me harder than a 30-06, and 7mm-08's that felt more like my 257Roberts. MILD.
I have a pal with a 308 that he loves. His next will be a 7mm-08 for his wife. He also wants a 243 and a 260 as well as a 358 down the road a ways. Why? Because a) he can afford it and b) he wants a rifle for each of the 308-based cartridges, without getting into wildcats.
To me, the only point in having more than one of any centerfire rifle in the lower 48 is to accomodate other family members, or purely "I want it". Paper ballistics do not fill the freezer. Being a hunter does. Any hunter can take any legal centerfire rifle and fill the freezer. Anything else in "conversation". Fine chat, here.
Regards,
Sweetwater