The 105 gr bullets from BOTH rifles are extremely accurate to 1000 yards and a bit further for the 6/284 because of the additional velocity that one can achieve.
The 243 would be a better choice if "many" rounds are to be fired and you want the barrel to last longer.
Personaly I like the 243 win. Any of the "improved" versions of that or the 6mm rem do well also. .243's are easy to find, easy to shoot, easy to get ammo if you desire to go that route and they are very accurate and effective.
I have a 6/06 with a 30" bbl and a 8 twist that pushes the 105gr A-max to 3400fps.. This gun is deadly on chucks to about 1300 or so.. I also agree on the .243 that is prolly my favorite 6mm..
7mm rem mag,6mm AI, 6mm rem, .223 6mm AI page
For your average shooter, I would suggest a .243, but for someone serious, I would start with 6mm and consider the 6x284 and .240 weatherby too. I like a slower twist with the 6mm and a fast twist for the 6-284 as it can better capatalize on the heavy bullets.
6mm-06 30 inch 3 groove Lilja barrel 8 twist Remington long action in a McMillan varmint model stock.Lapua 30-06 brass loaded with 57 grains of H1000 and a Fed 210 primer shooting plain Sierra 107's at 3433 fps.
Lynn