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_*_) through spectral energy distribution (SED) fitting, and we find that the hosts M_*_ of type 1 AGNs tend to be slightly smaller than those of type 2 AGNs by {Delta}logM_*_~0.2dex (~4{sigma} 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 the cosmic environment, and we find that the surface number densities (sub-Mpc) and cosmic-web environments (~1-10Mpc) are similar for both populations. In summary, our analyses show that the host galaxies of type 1 and type 2 AGNs have similar SFRs and cosmic environments in general, but the former tend to have a lower M_*_ than the latter. The difference in M_*_ indicates that the AGN unification model is not strictly correct, and both host galaxy and torus may contribute to the optical obscuration of AGNs.