That is a great question actually. Everyone says piston and diaphragm regs breathe the same, but we are talking about extreme depths. So I am curious too. The DIR divers, for example some prominent WKPP divers, used to emphasise that the DS4 was fine for them, as in "good enough". I never heard complains through the last two decades as seemingly the majority of deep divers switched to diaphragm regs. But like you, I'd love to hear if anyone felt any difference.
We should also consider the use as stage tanks vs backgas, since my understanding is that a travelling stage in a cave at depth can be breathed down to low tank pressure, where I wonder if flow rate differences at low(er) tank pressure can come into play. With backgas we should be back in the shallows when we hit 500 PSI, but not stages, I think?