The unified model of active galactic nuclei (AGNs) proposes that different AGN optical spectral types are caused by different viewing angles with respect to an obscuring torus. Therefore, this model predicts that type 1 and type 2 AGNs should have similar host-galaxy properties. We investigate this prediction with 2463 X-ray selected AGNs in the COSMOS field. We divide our sample into type 1 and type 2 AGNs based on their spectra, morphologies, and variability. We derive their host-galaxy stellar masses ($M_star$) through SED fitting, and find that the host $M_star$ of type 1 AGNs tend to be slightly smaller than those of type 2 AGNs by $Deltaoverline{mathrm{log}M_star}approx0.2~mathrm{dex}$ ($approx 4sigma$ significance). Besides deriving star-formation rates (SFRs) from SED fitting, we also utilize far-infrared (FIR) photometry and a stacking method to obtain FIR-based SFRs. We find that the SFRs of type 1 and type 2 sources are similar once their redshifts and X-ray luminosities are controlled. We also investigate cosmic environment, and find that the surface number densities (sub-Mpc) and cosmic-web environments ($approx 1text{--}10$~Mpc) are similar for both populations. In summary, our analyses show that the host galaxies of type 1 and type 2 AGNs have similar SFR and cosmic environment in general, but the former tend to have lower $M_star$ than the latter. The difference in $M_star$ indicates that the AGN unification model is not strictly correct and both host galaxy and torus may contribute to the optical obscuration of AGNs.
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