In order to better understand the nature of post-starburst quasars (PSQs) in the context of galaxy evolution, we compare their properties to those of post-starburst galaxies and quasars from appropriately selected samples possessing similar redshift (z ∼ 0.3), luminosity (M r ∼ −23), and data quality. We consider morphologies, spectral features, and derived physical properties of the stellar populations and central supermassive black hole. PSQs themselves come in two types: the more luminous AGNs with more luminous post-starburst stellar populations hosted by elliptical galaxies, some which are clearly merger products, and the less luminous systems existing within relatively undisturbed spiral galaxies and possessing signs of a more extended period of star formation. Post-starburst galaxies (PSQs) have elliptical and disturbed/postmerger morphologies similar to those of the more luminous PSQs, display similar spectral properties, but also can have younger stellar populations for a given starburst mass. Quasars at similar redshifts and luminosities around the Seyfert/quasar transition possess similar AGN characteristics, in terms of black hole mass and accretion rate, compared with those of PSQs, but do not appear to be hosted by galaxies with significant post-starburst populations. Recent studies of more luminous quasars find hosts consistent with those of our luminous PSQs, suggesting that these PSQs may be in transition between post-starburst galaxies and a more luminous quasar stage when the post-starburst stellar population remains dominant. The lower luminosity PSQs appear to differ from lower luminosity quasars (Seyfert galaxies) in terms of more significant star formation in their past.