  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.
