HINT - Caliber has little to do with making a good shot.
A .30-06 is more than enough for a 600yd shot on a deer. A 180gr Berger VLD hunting or a 180gr TSX will have plenty of energy at those distances out of the old '06. Learn to reload, to select the proper bullet for your application, and then learn how to deliver it with ethical accuracy at your intended distance. I'm not the worst shot at those distances but even I can't hold steady enough for a sure kill past 450yds unless the position is solid (most likely prone).
I agree with Ritten. My long range gun is a 7mm08. I have guns that shoot "flatter" than it does, but none are as accurate. If you know the distance to the target, and you know the capabilities of your rifle, the only thing else that is needed is the ability to place the shot. Remember, "bullet energy is deadly, but accuracy is fatal".