  This paper explores core-collapse supernovae as crucial targets for neutrino
telescopes, addressing uncertainties in their simulation results. We
comprehensively analyze eighteen modern simulations and discriminate among
supernova models using realistic detectors and interactions. A significant
correlation between the total neutrino energy and cumulative counts, driven by
massive lepton neutrinos and oscillations, is identified, particularly
noticeable with the DUNE detector. Bayesian techniques indicate strong
potential for model differentiation during a Galactic supernova event, with HK
excelling in distinguishing models based on equation of state, progenitor mass,
and mixing scheme.
