I think this comes down to 2 calibers. The 30-06 is the most versatile round out there. It has been around a long time and is very popular. However the .308 replaced the 30-06 in military service 60 years ago. It is considered to be more accurate and is in current military service.
You said shoot out to 1000 yards and honestly there aren't many people out there that can do that. Most of a bullet's energy is gone at that kind of range so if you want to do more than punch paper go with a bigger round. Now for punching paper at that range I say go with the .308 but you won't find a $400 rifle that is good to go 1000 yards with. Now if you start with a $400 rifle then spend another $200 on the trigger, then another $300-1000 on bedding, free-floating, lapping lugs and possibly even replacing the barrel with something match grade, and then $1000-5000 for your scope, then you might start hitting paper at 1000 yards. I really don't see many people that have ever shot 1000 yards, and the ones that have, spent several thousand on their guns.
Now all that aside, I find the .308 to be a better caliber than the 30-06. The few hundred fps that you gain with a 30-06 is not worth the loss in accuracy or the fact that .308 is in current military use so you will never run out of brass.