Sense you reload I really don't see any real difference in the two.
You can make either one do what the other one is capable of with little effort.
The 06 can be loaded down to a light 270 and the 270 can be loaded up to a pretty stout 06.
Either will take most anything you would hunt in the US and with the right load and good shot placement it will do fine in Canada and Africa.
I, my self have never cared for the 06 that much only because I don't hunt anything that the 270 can't handle and the extra recoil does nothing for my shoulder either.
Others will disagree I am sure but that is beatting a pretty dead horse.
Unless you are going after the big bears I would keep what you have.
I have two of them (a pre 64 and a 1988 model) and they have both served me very well over the years.
Now had you said a 270 WSM then that would be a different story.
I have three of those and none of them are for sale!!!
LONGTOM