As has already been said, yes, either of the two 120 gr. bullets will be fine in the 7mm-08. My whitetail buck this year was at 225 yds, entry just behind the near shoulder and exit was THROUGH the off shoulder. Plenty of penetration. 120 gr. Ballistic Tip at 3100 FPS. Nosler changed the BT Year’s ago after some failures when first introduced. Just be sure to buy the HUNTING bullet. They make both a hunting bullet and a varmint bullet.
The TTSX Barnes bullet expands much better than their old TSX and has also proven to be very accurate in my 7mm-08’s. Probably what I would choose for Elk. My suggestion would be to use whichever shoots the best in your rifle.
