There is nothing in this world that hasn't been killed with the '06.
Yup there are bigger, newer rounds out there, but I don't care how tough you are, the '06 (or my favorite the 270) works quite well and is easier to shoot.
In hunting you spend more time carrying your rifle then shooting it. I like light rifles for that reason (I admit, I'm old and lazy).
The easier the rifle is to shoot, the more you'll shoot it, the more you shoot it, the better shot you'll be.
Of the rifles you listed I think you'll be happier with the '06 in the long run.
As said I like the 270 Win but that wasn't on your list. I hunt elk with the 270 and it works great, so I have a hard time believing that the '06 with heavier bullets wont work.
Ammo is available anywhere and its extremely easy to load for.