In this study, we examine the single-scattering properties of aggregates of nano-sized spherical scattering centers (spherules) of different sizes and refractive indices, with an emphasis on contrasting the single-scattering properties of ordered and disordered aggregates, holding all other parameters constant. The ordered aggregates are constructed by arranging the spherules in a simple cubic configuration, while the disordered aggregates are constructed using an ideal amorphous solid algorithm. The single-scattering properties of both kinds of aggregates are computed using the superposition T-matrix method. We find that, in most cases, the scattering and absorption and hence extinction of radiation by ordered aggregates is stronger than for disordered aggregates: for the cases we examine, the average percent difference in scattering efficiency is 14%, and the maximum percent difference in scattering efficiency is 44%; the average percent difference in absorption efficiency is 5.3%, and the maximum percent difference in absorption efficiency is 18%; the average percent difference in extinction efficiency is 12%, and the maximum percent difference in extinction efficiency is 40%. These differences have implications regarding radiative transfer in systems of amorphous particles in general.