They shoot the same bullets, but the .30-06 shoots them faster. Accuracy has far more to do with the individual gun than caliber. Froget 1,000 yrds shot unless your are willing to spend more than $ 2,000. You can put togeather an accurate rifle for around $ 1,000, your scope will cost $ 800 and up then you will need a very good range finder and none in the under $ 500 range will do a good job out to 1,000 yrds. You can forget the range finder if your are shooting at none yardages. After you get the gun and work up the most accurate load you will need a drop chart and then you must go out and shoot at at least every 100 yards to check your chart. I built a .22-6mm up for long range coyote shooting. My final load will be between 3,400 and 3,500 fps. with an 80 gn. bullet. So far I have around 400 round down the tube and am still working on the load and the bullet. I have fired 1 group at 500 yards so far and it was a 3 1/4 in. 3 shot group in a 15 mph wind. Whoch bring up anpother thing you will need and that is a way to measure wind speed, wich can not only change speed several time in 1,000 yards but also direction. With a bullet that has a BC of .481 the bullet when fired at 3,481 fps will drop 137.21 inches at 800 yards and 159.12 in. at 850 yards at 1800 feet above sea level at 55 degrees. That is almost 22 inches, so you have to know the exact velosity of your bullet and the exact yardage of your target when you get out there. The difference between 950 yrds. and 1,000 yrds. is a drop of 83 inches. At the same elevation and temp, but if you change any thing you through off your drop chart. Warmer and it will shoot higher, colder and it will shoot lower. At higher elevations it will shoot higher and so on. To make matters worse you have the wind. With the above load the bullet will drift 38.58 inches at 800 yard with a 10 mph cross wind, and 64 1/2 in. at 1,000 yrds. so if you guess the wind at 10 and it is 15 mph your off 32 1/2 in at 1,000 yards.
If your after a 500 yard gun and have a reasonable range finder you will be able to do what is needed on game with any .308 or .30-06 that will shoot 1 moa. at that range, a 5 in group, if your are able to shoot that well.