The reason most sources say a 7mm-08 has lighter recoil is the optimum bullet weight is 139-140 grains. The 308 typically optimizes with a 162-165 grain bullet. This is not a "fair" comparison for recoil.
"If this is true maybe a 308 has a slight advantage because it has a very large premium bullet selection"? The 7mm bullets have a very large selection to choose from, the same as a.308.
The weight range for a 7mm-08 is 115 gr to 175 gr. The weight range for a 308 Win is 125 gr to 200 gr. As you can see, the larger bore diameter favors a heavier bullet, however there is a considerable overlap.
I would go along with Graybeard's analysis. If the muzzle velocity, bullet weight, and gun weight are the same, the recoil should feel the same.