If there's a prior in the community, my impression (as a neutrino physicist) is that if anything it's more toward Majorana than not, in the absence of evidence either way. It is surely nicer from a theory perspective, with a (seesaw) mechanism to help explain the very light neutrino masses, and lepton number violation that helps in the case for leptogenesis as an explanation for the universe's matter-antimatter asymmetry, etc. One way I think about it is that it's pretty interesting either way: Majorana demands physics beyond the Standard Model, while Dirac would seem to suggest that lepton number is more than an accidental symmetry of the Standard Model, implying some unknown quantum number. Meanwhile, many experimental searches for neutrinoless double beta decay go on, with many new/clever ideas to carve through the quite large allowed parameter space.