The main reason is that while black holes are more "extreme" objects, they are actually physically very simple. The matter collapses to a singularity (as far a

The main reason is that while black holes are more "extreme" objects, they are actually physically very simple. The matter collapses to a singularity (as far as we know), and so the physics is just described by the Einstein field equations with a correction for quantum fluctuations near the event horizon. Remarkably, the entire state of the black hole can be described by only the mass, charge, and angular momentum of the black hole. By contrast, although neutron stars are less "extreme", they end up in a regime where the physics becomes much more difficult. The gravity is strong enough that you still need general relativity, but because the object is extended rather than a singularity, there's also a bunch of "stuff" which needs to be described as well. This means that you need to add in quantum electrodynamics and quantum chromodynamics. Furthermore, it's thought that at these densities you end up with some sort of a superfluid which means you need fluid dynamics and statistical physics to model its behavior, all of which is extremely difficult. That said, there is another sense in which we could say that black holes are actually more mysterious than neutron stars. Although the physics of neutron stars is very complicated, we at least know what all the fundamental equations are. In the case of black holes if we want to understand physics near the singularity we would need a theory of quantum gravity which we currently don't have.