  We present a study of Spitzer/IRAC and X-ray active galactic nuclei (AGNs)
selection techniques in order to quantify the overlap, uniqueness,
contamination, and completeness of each. We investigate how the overlap and
possible contamination of the samples depends on the IR and X-ray depths. We
use Spitzer/IRAC imaging, Chandra and XMM X-ray imaging, and PRism MUlti-object
Survey (PRIMUS) spectroscopic redshifts to construct galaxy and AGN samples at
0.2<z<1.2 over 8 deg^2. We construct samples over a wide range of IRAC flux
limits (SWIRE to GOODS depth) and X-ray flux limits (10 ks to 2 Ms). We compare
IR-AGN samples defined using the IRAC color selection of Stern et al. and
Donley et al. with X-ray detected AGN samples. For roughly similar depth IR and
X-ray surveys, we find that ~75% of IR-AGN are identified as X-ray AGN. This
fraction increases to ~90% when comparing against the deepest X-ray data,
indicating that only ~10% of IR-selected AGN may be heavily obscured. The
IR-AGN selection proposed by Stern et al. suffers from contamination by
star-forming galaxies at various redshifts when using deeper IR data, though
the selection technique works well for shallow IR data. While similar overall,
the IR-AGN samples preferentially contain more luminous AGN, while the X-ray
AGN samples preferentially contain lower specific accretion rate AGN, where the
host galaxy light dominates at IR wavelengths. The host galaxy populations of
the IR and X-ray AGN samples have similar restframe colors and stellar masses;
both selections identify AGN in blue, star-forming and red, quiescent galaxies.
