As far as I can tell, there are two types of black sun coral out there that are being seen right now. T. diaphana, which seems to form small clumps of more upright polyps, and T. micrantha, which forms long thick tree-like branches.
It can be hard to tell which is which on small specimens, but micrantha has a poor survival history in captivity. They apparently need HUGE amounts of flow, above and beyond what regular sun corals need.
Diaphana seems much more forgiving, and IME seems pretty much identical in care to the orange/yellow species, but I have also only been keeping ANY sun coral since October. I haven't seen much specific literature on diaphana though; books either address orange/yellow sun corals (not hard to do if you feed them enough), or warns keepers to avoid micrantha because it seems to need something extra and no one is yet sure what.