I you reload it is 6 of 1, 1/2 dozen of the other. They are very similar in on game performance. If you are buying factory ammo I would go with the 06. 7mm Rem mag ammo is approx 50% more expensive when comparing the same type bullet.

I do lean toward the 30 caliber bullets or larger for bigger game like elk if I have a choice. As others have mentioned though you 270 will be a good choice for elk out to 400 yards with the right bullet.