The longer barrel will give you more velocity and there's a good chance that it'll be more accurate, but it affects the feel and handling of the weapon. A few extra fps won't do you any good if the gun feels clumsy in your hands while walking around in the woods. Every gun is different and how it feels is different for everyone. If your walking around out west where you're out in the open the longer barrel will work best. If you're walking around in a thicket where the barrel is getting caught on every other branch I'd go with the shorter barrel.

Another thing to think about now that I reread your post. The 30-06 uses a long action and the .243 uses a short action. The barrel on the .243 is 2" longer but the overall length of the gun is probably only about 1" longer. That's why the balance of every gun is different.