I don't understand what you mean by blackhole situation when a star becomes either a white dwarf or a neutron star it doesn't become a blackhole at the same time, it can only do one thing.
A white dwarf can burn for billions of years until its out of fuel, as it runs out the dwarf gets less hot and thus less bright. A neutron star was a white dwarf who collapsed in on itself (not becoming a black hole) but becoming a neutron stars which is full of tightly packed neutrons.
Which one lasts longer depends on how big the stars are etc: it differs in ever case.
