Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ_(ch)(r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.
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