Dynamical theory (DT) calculations have been successfully developed to explain neutron spin-echo resolved grazing-incidence scattering from diffraction gratings. The theory, without any adjustable parameters, has been shown in previous publications to accurately reproduce the sensitivity of the spin-echo polarization signal to sample specifications and scattering geometry. The phase-object approximation (POA), which is computationally less demanding than the DT, has also been used to analyze neutron spin-echo polarization data obtained from diffraction gratings. In this paper, POA and DT calculations are compared for neutron scattering from various diffraction gratings in different geometrical settings. POA gives a good description of the data for transmission cases, where the neutron beam is incident at large angles to the average grating surface. However, for the grazing-incidence reflection cases that were studied, the POA does not fit the data using the independently determined dimensions of the measured gratings. On the other hand, the good agreement between dynamical theory and the data from gratings with known profiles paves the way for its use to extract profile information from periodic samples with unknown structures.