Because the physical evidence for dark matter is its calculated gravitational effects, then it may be assumed that dark matter behaves similarly to baryonic matter with respect to the black hole. This follows because we have only a single theory of gravity that requires the identical behavior of all kinds of mass.
We can speculate on differences. Because the properties of dark matter are unknown, the details related to such principles as conservation of information cannot be assessed. In addition, as it approaches the black hole it may not show the same radiative behavior as baryonic matter.
Once the dark matter is within the black hole, I don't believe there are physics to describe any difference between it and baryonic matter.