If all else is the same, IMO you have to go to a .25-06 / .257 Bob for a meaningful step down in recoil. I just don't see that much of a difference from a .30-06 to a .308 or even a 7mm-08.
Now, you can always add rifle weight, a better pad, and maybe a better stock fit / design.
Respectfully disagree...
For a while I had two identical-pattern rifles, Remington LSS Mountain Rifles, one in 30-06 and one in 7mm-08. Still have both but the '06 is now a sporter-weight barrel.
Anyway, the 7-08 was most assuredly a meaningful step down in recoil from the 30-06. Rifles were identical except the 30-06 was a little heavier due to the longer action.
-jeff