The only advantage I can see to the 7-08 is the weight of the rifle due to the shorter action. A pound makes little difference to me so I've always prefered the 7X57. I have one built on a 98 Mauser action with an old Bishop stock and a Lyman 48 peep sight. It's my old school deer gun. Weighs 8lbs.
I disagree that the 7-08 is inherently more accurate than the 7X57, or the .280 for that matter. With good barrels on a good rifle all three can shoot more accurately than the shooter can hold.
I've never owned a .280 but if a deal came by on one I'd jump on it. It's a great cartridge built off the case of an equally great cartridge. Whats not to like? Its capable of taking any N. American game at ranges out to 400 yards or more. So is a 7X57 or a 7-08. Six of one, half a dozen of the other.