Pulsars are highly dense, rotating neutron stars that emit beams of electromagnetic radiation. While pulsars can be extremely bright in terms of the energy they emit, it's important to note that their brightness is concentrated into narrow beams rather than being spread out uniformly like the Sun's radiation.
In terms of luminosity, or total energy output, pulsars can be millions or even billions of times brighter than the Sun. This incredible brightness is due to the rapid rotation and immense magnetic fields of pulsars, which generate intense electromagnetic radiation.
This is because the radiation is concentrated into narrow beams that may not be aligned with our line of sight. If a pulsar's beam is not directed toward us, it will appear faint or even undetectable, despite its high luminosity.
Therefore, it's challenging to directly compare the brightness of a pulsar to the Sun, as it depends on the orientation of the pulsar's beam and our viewing angle.