I would go for the 30-06, unless 1.75 pounds makes that much difference to you on packing it in to the back country. You will have a little more range with better knock down power with the 06 over the 308 and a little bit better ammo selection if you are not a handloader.
If you took out the elk hunting, it would be hard to pass up the 308 selection with the lighter weight package. I am not saying the 308 will not bring down elk, but it is getting a little low in velocity pass 200 yards with heavier 180 grain bullets. My personal preference in bullets for the 308 is 150 grain, and 165 for the 06 as good all around bullet weights for deer to elk in Nosler partition or other similar constructed heavy duty bullet.
RELH