In the 7-08 I would suggest the 140 grain TSX.
Keep in mind that, because the 7-08 case is shorter than the 7x57, it doesn't provide as much room for powder with the long, heavy bullets (just like 165's are a better choice than 180's in the .308 while the heavier bullets work fine in the 30-06).
Stick to well-built 140's (TSX especially, or even a bonded bulllet) and you'll be able to maintain higher velocity/flatter trajectory while enjoying excellent penetration on bigger game. (I recently used the 140 TSX in a 7x57 on 300+ yard Kudu with complete penetration through the chest. I would expect it to work the same in the 7-08. I would not have been nearly as comfortable trying the shot with a 175 grain bullet.)