  We present the largest-scale comparison to date between observed
extragalactic X-ray binary (XRB) populations and theoretical models of their
production. We construct observational X-ray luminosity functions (oXLFs) using
Chandra observations of 12 late-type galaxies from the Spitzer Infrared Nearby
Galaxy Survey (SINGS). For each galaxy, we obtain theoretical XLFs (tXLFs) by
combining XRB synthetic models, constructed with the population synthesis code
StarTrack, with observational star formation histories (SFHs). We identify
highest-likelihood models both for individual galaxies and globally, averaged
over the full galaxy sample. Individual tXLFs successfully reproduce about half
of oXLFs, but for some galaxies we are unable to find underlying source
populations, indicating that galaxy SFHs and metallicities are not well matched
and/or XRB modeling requires calibration on larger observational samples. Given
these limitations, we find that best models are consistent with a product of
common envelope ejection efficiency and central donor concentration ~=0.1, and
a 50% uniform -- 50% "twins" initial mass-ratio distribution. We present and
discuss constituent subpopulations of tXLFs according to donor, accretor and
stellar population characteristics. The galaxy-wide X-ray luminosity due to
low-mass and high-mass XRBs, estimated via our best global model tXLF, follows
the general trend expected from the L_x - star formation rate and L_x - stellar
mass relations of Lehmer et al 2010. Our best models are also in agreement with
modeling of the evolution both of XRBs over cosmic time and of the galaxy X-ray
luminosity with redshift.
