Do neutron stars share more in common with stellar mass black holes than just density?

Toward the end of 2005, astronomers studying the results from NASA's Chandra x-ray observatory determined that a very massive star, in excess of 40 solar masses, collapsed to form a neutron star instead of an expected black hole.
One obvious implication of the results is evident; that many more stars than previously thought, are ending up as neutron stars.
It is as if Nature is telling us that this family of ultra-dense stellar objects, are more fundamental to the evolution of our Universe, than we might ever have imagined.

Neutron degenerate pressure, does not seem to be the end of the line though, before gravity causes a runaway implosion toward the 'singularity' lurking beneath the event horizon of a Kerr stellar black hole.
Such evidence can be speculated to imply that upon reaching its maximum degenerate pressure, the super-dense nucleon fluid at the core of a neutron star, might change its properties, from fermionic behaviour to bosonic behaviour.
Various physicists have used computed simulations to support evidence for postulated 'quark stars' or even 'electroweak stars', where quarks have decayed into leptons such as electrons and neutrinos which allow for a higher outward pressure to counter gravitational collapse.
However, these are all still fermions, and as such, are subject to Pauli's Exclusion Principle.
If the fluid of the core took on bosonic properties, the particles will behave according to Bose-Einstein statistics.

So, the s-matrix of the system that is a neutron star, is proving to contain far more probable solutions than might have previously been overlooked.