Half a poiund of one or six of the other...there is basically no difference between the two..the .308 will handle heavier slugs but with not much velocity.. 140 vs 150 for deer...I don't think the chest cavity of a whitetail or black bear would much notice...
I've had both of them and currently am not really enamored with either. I like long action cartridges far more. But if I had to choose between the two I'd pick the 7-08 because it's a flatter shooting round. But I'd so much rather have a .280 or a 7 mag.
I bought my 14 year old son a 308 3 years ago. He shoots Barnes 168 Gr. loads out of it, and with 3 pulls of the trigger on deer he connected on all of them with none going further then 30 yds. Great round, great knock down power and a fine shooting and easy to handle gun.
I have them both and use the 7mm08 more often. Haven't had a deer take a step after being shot with it. The 308 hasn't done bad but I have had to track a couple. It very well could be the difference in the bullets I'm using in them though.
I have a 308 in a Rem Model 7 and 2 of my buddies have the same model in the 7mm-08. We all have taken deer cleanly over the years and love that model gun to carry. But when it comes to buying ammo, they usually pay more for theirs. I know they also shoot alot of reloads. I have the same problem with my 280 rem. I love my 700 mtn rifle chambered in it but never get deals on ammo. My buddies who have 30-06 and 270's can find their ammo cheaper and more available. It just comes down to the type of hunter or shooter you are. If you like to shoot a lot and usually go to Wal mart or dicks sporting goods, stick with the 308. IF you're the opposite go with the 7mm-08. I don't think you'll be disappointed with the performance of either caliber that you choose.
Bought a 7600 chambered in 7mm-08 years ago for my sons 1st year of deer. We purchased a stock blank which we cut down and mounted for him. The 08 had has a variety of loads that the reloader can work with. I rembered my 1st gun which was the 30-30 with a steel butt plate. I made his starting loads mild enough so that he was able to hit the target without flinching. His buck that 1st year was a large 8 point that beat my best one.
I think that the 7mm-08 was designed with deer hunters in mind...Mine simply flattens deer and I can't explain why..Most of the time when I use another rifle, a deer wil run 20-30 yards with a solid hit..With the 7mm-08, they just drop.