I wish to describe in simple but correct terms the analogy between the Cabibbo–Kobayashi–Maskawa (CMK) and Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrices. The CMK matrix describes the rotation between weak interaction eigenmodes and the flavour (mass?) eignstates of quarks. The PMNS matrix is the rotation between neutrino flavour states and the time-evolution (mass) eigenstates. Both are unitary and experimentally known.
Are the following two statements correct?
Quark masses are large compared to amplitudes of the flavour-mixing weak interaction, thus the effect of flavour oscillations is negligible (and manifested mainly as decays of higher-mass quarks in the weak channel). On the other hand, the differences in neutrino eigenenergies are comparable to the mixing amplitudes thus the contrast of oscillations is high.
The interaction responsible for the CMK matrix is the weak interaction, while the interaction responsible for PMNS and neutrino oscillations is unknown (?) due to non-observability or any other of its effects.
This answer sheds some very useful light on point no. 2, but I'm not sure whether the "non-renormalizable dimension 5 operators" mentioned there can be unambitious classified as different (in some well-defined sense) from the weak interaction or not.