I'd doubt that any deer would be able to tell the difference between the 7mm-08 and the 308. Both are excellent cartridges. The lighter bullets the 7mm chucks downrange makes for lighter recoil from same size cases. Lots of metal target guys like the 7mm-08.
Is there an advantage between the 7mm and 30 caliber, it's like folks that argue over which is best between the 270 and the 30-06. Both of those are great deer cartridges and so is the 308 and 7mm-08.
Now if you want a real deer cartridge it's the 280 Remington!