  We present a complete comparison of semi-inclusive $\nu_\mu$-$^{12}$C
cross-section measurements by T2K and MINER$\nu$A collaborations with the
predictions from the SuSAv2-MEC model implemented in the neutrino-nucleus event
generator GENIE and an unfactorized approach based on the relativistic
distorted wave impulse approximation (RDWIA). Results, that include cross
sections as function of the final muon and proton kinematics and correlations
between both, show that the agreement with data obtained by the RDWIA approach,
that accounts for final-state interactions, matches or improves GENIE-SuSAv2
predictions for very forward angles where scaling violations are relevant.
