I got a 30-06 because that's what my Dad had, and I got a bunch of ammo, brass and bullets from him. So, my start-up costs were less.
Besides the wider selection in 30 caliber bullets, brass was everywhere... and in backwater towns you are more likely to find 30-06 on the back counter than 270. Never made any difference to me because I loaded my own and took plenty, but everyone carries 30-06.
If I had a choice to make today, I'd probably pick a nice 280 Remington over either the 270 or the 30-06 for deer, antelope, elk and black bear.
Like other posters here, though, I have hunted side-by-side with other hunters and I have seen no real difference in dropping deer and elk out to 400 yards with any standard caliber.
The 30 mags do a better job at distance than the '06 offspring on elk, but I haven't seen a 7mm mag do any better than '06, 270 or 280 Remington, either.
If I want something more for big game, I stick with the '06 case and step up to 338-06. Something to be said for a case that necks up or down and makes great hunting calibers from 243-06 up to 35 Whelen.