All 3 are capable of very good- INCREDIBLY good- long range accuracy. IMNSHO, the 30-06 enjoys a slight edge due to increased energy over the .308, and a better BC over the 25-06. In the hands of the average to better than average shooter, you would never see the difference. In the hands of an experienced military sniper trying for that 1200 meter shot, the 30-06. The .270 also is in the "right up there" category- but the guys competing for world record tight groups at very long ranges are using none of those 4- they are shooting 6mms. The ability to shoot at distances measured in zip codes is PARTIALLY related to the caliber and rifle. The ability of the shooter to read wind, mirage, range, target speed, elevation, etc ad ifinitum will also come into play.
What we have here is... failure- to communicate.