The magnetic order/disorder of the Cr moments in the antiferromagnetic state of the ferrimagnet $\mathrm{NiC}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$ is reinvestigated by neutron powder diffraction to clarify the observation of reduced Cr moments located on a pyrochlore-like lattice [M. Reehuis et al., Phys. Rev. B 91, 024407 (2015)]. The change of the spin structure in the slightly Cu-doped chromite $\mathrm{N}{\mathrm{i}}_{0.98}\mathrm{C}{\mathrm{u}}_{0.02}\mathrm{C}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$ has been studied as well, where orthorhombic lattice distortions become stronger. For both chromites we observe at 2 K two magnetic phases: one with two propagation vectors $\mathbit{k}=$ (0,0,1) and (0,0,${k}_{z}$), and a second one with $\mathbit{k}=$ ($1/2,1/2,1/2$). The latter phase disappears at 21 K for $\mathrm{NiC}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$ and at 24 K for $\mathrm{N}{\mathrm{i}}_{0.98}\mathrm{C}{\mathrm{u}}_{0.02}\mathrm{C}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$. Data analysis shows that the two phases reside on two disparate Cr sublattices. These are identified by different chain directions of strongly bonded spin pairs along diagonals in the pseudotetragonal ${a}_{1}{a}_{2}$ plane. The less distorted $\mathrm{NiC}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$ shows the same subdivision of the lattice still with a saturated Cr moment for the (0,0,1)/(0,0,${k}_{z}$) phase, however, with a strongly reduced moment for the ($1/2,1/2,1/2$) phase, whereas an almost saturated moment shows up in the Cu-doped chromite. The reduced moment in $\mathrm{NiC}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$ indicates disorder on one Cr sublattice down to low temperature due to stronger frustration on the less distorted tetragonal pyrochlore lattice. Magnetoelastic effects and further neighbor spin interactions are mainly considered in the discussion of the observed peculiar ordering processes. Notable is the transition temperature of the ($1/2,1/2,1/2$) phase of $\mathrm{NiC}{\mathrm{r}}_{2}{\mathrm{O}}_{4}$ around 21 K, where anomalies for the specific heat and for the magnetodielectric behavior have recently been reported [T. D. Sparks et al., Phys. Rev. B 89, 024405 (2014)].