Like everyone said they are basically the same. The '06 has the advantage of a little more velocity and a wider bullet selection. The .308 is shorter and in most cases more accurate (perferred military sniper round). So either one of those choices will be fine but if you are set on a lever action then I would have to go with the .308 because it is 12 mm shorter and when that big buck in running through the woods (possibily the only deer you will see on your hunt from what I have read) you are going to want the shortest reload time you can have. Thats why i would go with the .308, plus the fact that I have a .308 doesn't hurt either!!

Either way that deer won't know what hit it when the bullet finds it's mark behind the shoulder.