Case and point:
Swift A-Frames. They always mushroom correctly. It's in their nature. 100%
Partitions "usually" work. Look at these recoveries. They jacket separated. They shredded. They worked. But randomization does occur.
While better in practice, Barnes TTSX should "usually" work but you're relying on the mechanical opening of the petals. If one petal breaks off, it may not work quite so perfectly. Still very good, but the mechanical opening of a barnes petal is less than 100% compared to the mushroom of an A-Frame that is guaranteed.
With random distribution of chance and failure to open as desired, I would prefer a controlled expansion mushroom to a mechanical opening feature of a partition or barnes on dangerous game. It's my preference. For plains game, I can see the flatter shooting of a barnes to be preferred over heavier partitions, and am on the fence on say 140gr 7mm barnes versus 175gr 7mm A-frame. (again, small bore comparisons)
To date, no failures with barnes. No failures with A-frames. Some failures with partition. The photo suggests why that may be the case.