A 165 mono bullet like a TSX doesn't make a .308 "Bigger", it makes it "Deeper". Whether that is an advantage depends on whether you suppose the .308 had a penetration problem, or a bullet destroying problem in the first place. Its difficult to fix something that isn't broken.
The 168 TSX at 30-06 speed isn't much different than the same bullet or the 165 at .308 speed, and the differences are just a matter of being a few yards farther or closer to make things even up. It just happens to be a bullet that I have extensive experience with on population control culls in Australia. There isn't any question that it penetrates more than typical cup and core bullets, its more of a question of whether that is an advantage or not. The reality is that in most cases it isn't. When you trade a wide hole for a deep hole, you better make sure that you needed a deeper one because the narrower wounder channel of the deepest penetrating bullets works against you the rest of the time. We took out hundreds of animals per week, and believe me Barnes was used as a swear-word much of the time. Logistics being what they are, they ended up getting used up in the end but not happily. They ended up with a firm lock on last place.
Thick skinned game changes things around somewhat, but there's plenty of better bullets with the lead still in them for that too.