I've had excellent results with Barnes TTSX 168 grain (out of a .308) and TSX 150 grain (out of a .30-30). I believe that part of why I've had such great results is that all of the game was taken at 100 yards or less, so velocities were quite high for those cartridges.
Now that I'm looking at elk and muleys in the West, I'm very conscious that the distances for likely shots are opening up. Something that surprised me was looking at the expansion that Nosler shows at various speeds for their bullets. Specifically I compared the expansion of their E-Tip copper versus the partition versus accu-bond:
E-tip:
Partition:
Accubond:
Given the initial velocity out of a shorter barrel from a .308 is rather modest, I would be hesitant to use a copper monolithic on elk when it drops below 2200 - which will likely be at 200 yards for my application. To my mind, the Accubond and especially the Partition see to demonstrate appropriate expansion down to a much lower velocity than the monolithics.