The issue is rather that we don't know what all that star stuff becomes once it goes into the black hole, though there are theories. The problem is that the defining feature of a black hole, its even horizon, by necessity means there is no way of knowing what theory is correct since nothing happening inside is supposed to matter to us.
So before we can make any real progress on the interior of black holes we thus need to figure out exactly in what sense the event horizon leaks information, if it does.
In contrast, while we don't really know what happens to matter inside a neutron star, its surface remains visible to us and so we have been able to discard many different theories about what goes inside it. There is still debate about the precise equation of state, which correspond to different internal structure the various models represent and so different ideas of how a neutron star is made up.
Honestly, I don't know how much difference there are between the various models, but pretty crazy sounding ideas are still popping up, so there must be at least some space left.