It turns out to be very difficult, for a variety of technical reasons, to determine the hierarchy of the neutrino masses, although it is not impossible to figure it out experimentally. As a result we don't have a definitive answer yet, but we should soon. "Multi-megaton scale under ice (or water) detecting atmospheric neutrinos with low energy threshold may establish the mass hierarchy with high confidence level in few years."
Enhancements of experiments at existing facilities would permit us to determine "the angle delta_CP, and resolve the mass hierarchy at 3-sigma for 35% of the possible delta_CP values." With adequate fund, by "the end of the decade, this should push the error on delta_CP to 15-28 degrees, and this is not systematics limited."