.... or we can discuss if 500 yard shooting is actually hunting LOL
Either caliber will do it, neither will do it particularly well. In field conditions you'll want to shoot a VLD @ 2900-3000fps. With 30 cal it puts you into magnums; or you can step down a caliber or two and save a shoulder.
x2....I knocked a deer dead in its tracks last year with a .308 with cheapo federal softpoint ammo. He dropped like a bag o taters,but i was also at bowhunting range maybe 20ft tops lol
The 308 is only equivalent to the 30/06 if the 308 pressure is a bit higher. There is no reason either couldn't be good on deer to 500 yards as long as you're competent enough to allow for trajectory. I've killed deer with both and they were just as dead with both.
With the choice between the two, decide if you want a short action or long action. The other differnces are nominal. The '06 is going to be a little faster but not much.