RE: 7mm-08 vs 308
I'd go with the 7-08. At least, of the calibers you listed.
Since you are shooting a fine, European sporting rifle, I would pair it with a fine, European sporting cartridge, 7x57. Of course, you are basically accomplishing the same thing as a 7-08, and there are more and better factory offerings for the 7-08 these days. But you see what I am getting at.