Are you sure the 7mm-08 is faster than the .308? My Lyman 48'th manual (closest one within reach) is showing .308 a touch faster than 7mm-08 with comparable bullet weights.
168 grain with RX15 max load is listed as 2628 fps for 7mm-08 and 2724 fps for .308.
154 grain on 7mm, max load with IMR-4064, is listed as 2702 fps. 155 grain on .308, max load with IMR-4064, is listed as 2885 fps.
I picked the powders based on the 7mm-08 recommended accuracy load in the manual, but the trend appears to be consistent. Do the hunting loads buck the trend?
To be clear, there's nothing wrong with the 7mm-08, it's a fine hunting cartridge. I was under the impression that it has less felt recoil than .308.