Symmetry, structural features, and point defects in the Czochralski-grown single crystals with the initial compositions CeSc3(BO3)4 (CSB-1.0) and Nd1.25Sc2.75(BO3)4 (NSB-1.25) are studied by the full-profile Rietveld method on synchrotron X-ray powder data. The space group P321 is first established and confirmed for CSB-1.0 and NSB-1.25 crystals, respectively. The features of synchrotron diffraction patterns that distinguish the space group Р321 from the R32 one are given. The site occupancies in both structures are refined and resulted in the stoichiometric composition for CeSc3(BO3)4, which coincides with the nominal composition, and the composition [Nd0.455(1)Sc0.045(39)(1)]Nd0.500(2)Sc3(BO3)4 ((Nd0.955Sc0.045(39))Sc3(BO3)4), which differs from the initial Nd1.25Sc2.75(BO3)4 one, with partial occurrence of Sc ions in one of the trigonal-prismatic sites. An analysis of literature data on single crystals with the general formula RESc3(BO3)4 (RE = Ce, Pr, Nd) together with the results of present study of powdered single crystals gives reason to exclude a crystallization of these compounds and solid solutions based on them in the space group R32. The correlation between the refined compositions of RESc3(BO3)4 crystals (RE = La, Ce, Pr, Nd), having a specific space group, and compositions of initial charge is given.