When I first started shooting matches the 7mm-08 was still a wildcat. The reason it caught my eye was that I loved a 7x57 rifle I had built and it was very accurate and I was hoping to replicate that with the 7-08 and pretty much did they are almost ballistic twins. Accuracy wise 7-08 vs 308 they are about the same... both very good. You have to get out to 700+ yards IMO to really start talking about any ballistic advantage between the two. There is really no real world advantage to 7-08 at your typical hunting yardages IMO. You get a very slight reduction in recoil and that's about it.
You take both. Get out 2 boxes of Sierra bullets. Load the .308 with a 165 and the 7-08 with a 140. In either this will kill the crap out of any whitetail you come across with ZERO issue. That is a 1 and done loading for any rifle chambered in these as long as you can get the gun to shoot which has never been a problem for me with these two cartridges. May have run across 1-2 crappy guns but this has never been these loads fault.
I've killed a train car load of deer with both of these. No magnum needed... If you want a no-nonsense proven all around whitetail killer for our woods..... this is it.
Flip a coin you can't go wrong with either IMO as long as you shoot the right bullet weight.