  The sensitivity of X-ray facilities and our ability to detect fainter active
galactic nuclei (AGNs) will increase with the upcoming Athena mission and the
AXIS and Lynx concept missions, thus improving our understanding of
supermassive black holes (BHs) in a luminosity regime that can be dominated by
X-ray binaries. We analyze the population of faint AGN (L_x (2-10 keV) < 10^42
erg/s) in the Illustris, TNG100, EAGLE, and SIMBA cosmological simulations, and
find that the properties of their host galaxies vary from one simulation to
another. In Illustris and EAGLE, faint AGN are powered by low-mass BHs located
in low-mass star-forming galaxies. In TNG100 and SIMBA, they are mostly
associated with more massive BHs in quenched massive galaxies. We model the
X-ray binary populations (XRB) of the simulated galaxies, and find that AGN
often dominate the galaxy AGN+XRB hard X-ray luminosity at z>2, while XRBs
dominate in some simulations at z<2. Whether the AGN or XRB emission dominates
in star-forming and quenched galaxies depends on the simulations. These
differences in simulations can be used to discriminate between galaxy formation
models with future high-resolution X-ray observations. We compare the
luminosity of simulated faint AGN host galaxies to observations of stacked
galaxies from Chandra. Our comparison indicates that the simulations
post-processed with our X-ray modeling tend to overestimate the AGN+XRB X-ray
luminosity; luminosity that can be strongly affected by AGN obscuration. Some
simulations reveal clear AGN trends as a function of stellar mass (e.g., galaxy
luminosity drop in massive galaxies), which are not apparent in the
observations.
