The directional energy spectrum of neutrons generated from the in-flight fusion reaction of 1-MeV tritons contains information about the hot-spot symmetry. The National Ignition Facility (NIF) fields Symmetry Capsule (Symcap) implosions, which have historically measured the symmetry of the radiation, drive by measuring the hot-spot shape via x-ray self-emission. Symcaps are used to tune the hot-spot symmetry for ignition experiments at the NIF. This work shows the relationship between directional secondary DT-n spectra and x-ray imaging data for a large database of Symcap implosions. A correlation is observed between the relative widths of the DT-n spectra measured with nTOFs and the shape measured with x-ray imaging. A Monte Carlo model, which computes the directional secondary DT-n spectrum, is used to interpret the results. A comparison of the x-ray and secondary DT-n data with the Monte Carlo model indicates that 56% of the variance between the two datasets is explained by a P2 asymmetry. More advanced simulations using HYDRA suggest that the unaccounted variance is due to P1 and P4 asymmetries present in the hot spot. The comparison of secondary DT-n data and x-ray imaging data to the modeling shows the DT-n data contain important information that supplements current P2 measurements and contain new information about the P1 asymmetry.