We have measured the glassy-state structural relaxation of aqueous suspended polystyrene (PS) nanoparticles (the case of soft confinement) and the corresponding silica-capped PS nanoparticles (the case of hard confinement) via differential scanning calorimetry. Suspended and capped PS nanoparticles undergo physical aging under isobaric and isochoric conditions, respectively. With decreasing diameter, suspended and capped PS nanoparticles exhibited reduced and bulk glass transition temperatures (T(g)), respectively. To account for T(g) changes with confinement, all physical aging measurements were performed at a constant value of T(g) - T(a), where T(a) is the aging temperature. With decreasing diameter, aqueous suspended PS nanoparticles exhibited enhanced physical aging rates in comparison to bulk PS. Due to differences in thermodynamic conditions during aging and interfacial effects from nanoconfinement, at all values of T(g) - T(a) investigated, capped PS nanoparticles aged at reduced rates compared to the corresponding aqueous suspended PS nanoparticles. We captured the physical aging behavior of all nanoparticles via the Tool, Narayanaswamy, and Moynihan model of structural relaxation.