  We compare the relative merits of AGN selection at X-ray and mid-infrared
wavelengths using data from moderately deep fields observed by both Chandra and
Spitzer. The X-ray-selected AGN sample and associated optical follow-up are
drawn from the SEXSI program. Mid-infrared data in these fields are derived
from Spitzer imaging, and mid-infrared AGN selection is accomplished primarily
through application of the IRAC color-color AGN `wedge' selection technique.
Nearly all X-ray sources in these fields which exhibit clear spectroscopic
signatures of AGN activity have mid-infrared colors consistent with IRAC AGN
selection. These are predominantly the most luminous X-ray sources. X-ray
sources that lack high-ionization and/or broad lines in their optical spectra
are far less likely to be selected as AGN by mid-infrared color selection
techniques. The fraction of X-ray sources identified as AGN in the mid-infrared
increases monotonically as the X-ray luminosity increases. Conversely, only 22%
of mid-infrared-selected AGN are detected at X-ray energies in the moderately
deep (~100 ks) Chandra data. We hypothesize that the IRAC AGN that lack X-ray
detections are predominantly high-luminosity AGN that are obscured and/or lie
at high redshift. A stacking analysis of X-ray-undetected sources shows that
objects in the mid-infrared AGN selection wedge have average X-ray fluxes in
the 2-8 keV band three times higher than sources that fall outside the wedge.
Their X-ray spectra are also harder. It is evident from this comparative study
that in order to create a complete, unbiased census of supermassive black hole
growth and evolution, a combination of sensitive infrared, X-ray and hard X-ray
selection is required. We conclude by discussing what samples will be provided
by upcoming survey missions such as WISE, eROSITA, and NuSTAR.
