This is an interesting question, and probably one that Stan Woolsey and his colleagues could answer.
Well consider the masses, and Type II would have an advantage, but Type Ia magnitudes are perhaps brighter, indicating a higher reaction density. And then one has to look at the reactions from which neutrinos are formed. Perhaps there is an overlap between heavy Type I's and lighter Type II's - and by heavy, I mean at the top of the population of mass distribution.
I briefly went scanning for neutrino fluxes or densities, but couldn't find anything definitive.