We have analyzed archival \textit{Chandra} and \textit{XMM-Newton} data for two nearly complete homogeneously selected samples of type 2 Seyfert galaxies (Sy2s). These samples were selected based on intrinsic Active Galactic Nuclei (AGN) flux proxies: a mid-infrared (MIR) sample from the original IRAS 12\(\mu\)m survey and an optical ([OIII]\(\lambda\) 5007 \AA\ flux limited) sample from the Sloan Digital Sky Survey (SDSS), providing a total of 45 Sy2s. As the MIR and [OIII] fluxes are largely unaffected by AGN obscuration, these samples can present an unbiased estimate of the Compton-thick (column density N\(_H > 10^{24}\) cm\(^{-2}\)) subpopulation. We find that the majority of this combined sample is likely heavily obscured, as evidenced by the 2-10 keV X-ray attenuation (normalized by intrinsic flux diagnostics) and the large Fe K\(\alpha\) equivalent widths (several hundred eV to over 1 keV). A wide range of these obscuration diagnostics is present, showing a continuum of column densities, rather than a clear segregation into Compton-thick and Compton-thin sub-populations. We find that in several instances, the fitted column densities severely under-represent the attenuation implied by these obscuration diagnostics, indicating that simple X-ray models may not always recover the intrinsic absorption. We compared AGN and host galaxy properties, such as intrinsic luminosity, central black hole mass, accretion rate, and star formation rate with obscuration diagnostics. No convincing evidence exists to link obscured sources with unique host galaxy populations from their less absorbed counterparts. Finally, we estimate that a majority of these Seyfert 2s will be detectable in the 10-40 keV range by the future NuSTAR mission, which would confirm whether these heavily absorbed sources are indeed Compton-thick.