We present a comparative study of differential cross sections (DCSs) and spin polarizations for positron scattering from C60 and A@C60, elucidating the role of encapsulation of rare gas atoms inside the giant C60 cage. A comparison is provided with the earlier work for elastic positron-C60 scattering. We find a very good agreement even when a model potential is used for the positron-C60 interaction. Also, we evaluate similarities and differences between the positron and electron DCSs and spin polarizations, both from bare and endohedral targets. To mark resonance features on the scattering dynamics, DCSs and spin polarizations are calculated at resonant energies, which showcase different characteristics compared to the cases where the positron energy is non-resonant. In order to account for a complete picture of the scattering process, an absorption potential is included in the total scattering field. For the sake of illustrating the impact of individual interactions and their interplay as a whole, DCSs and spin polarizations are reported including several scattering interactions alternatively.