Modern cosmological simulations heavily rely on feedback from active galactic nuclei (AGN) in order to stave off overcooling in massive galaxies, and galaxy groups and clusters. Given that AGN are a key component of such simulations, an important independent test is whether or not the simulations capture the broad demographics of the observed AGN population. However, to date, comparisons between observed and simulated AGN populations have been relatively limited. Here, we have used the cosmo-OWLS suite of cosmological hydrodynamical simulations to produce realistic synthetic catalogs of X-ray AGN out to z = 3, with the aim of comparing the catalogs to the observed X-ray AGN population in the XXL survey and other recent surveys. We focused on the unabsorbed X-ray luminosity function (XLF), the Eddington ratio distribution, the black hole mass function, and the projected clustering of X-ray AGN. To compute the unabsorbed XLF of the simulated AGN, we used recent empirically-determined (luminosity-dependent) bolometric corrections, in order to convert the simulated bolometric luminosity into an observable X-ray luminosity. We show that, using these corrections, the simulated AGN sample accurately reproduces the observed XLF over 3 orders of magnitude in X-ray luminosity in all redshift bins from z = 0 out to z = 3. To compare to the observed Eddington ratio distribution and the clustering of AGN, we produced detailed “XMM-Newton-detected” catalogs of the simulated AGN. This requires the production of synthetic X-ray images extracted from light cones of the simulations, which self-consistently contain both the X-ray AGN and the emission from diffuse, hot gas within galaxies, galaxy groups, and clusters and that fold in the relevant instrumental effects of XMM-Newton. We apply a luminosity- and redshift-dependent obscuration function for the AGN and employ the same AGN detection algorithm as used for the real XXL survey. We demonstrate that the detected population of simulated AGN reproduces the observed Eddington ratio distribution and projected clustering from XXL quite well. Based on these comparisons, we conclude that the simulations have a broadly realistic population of AGN and that our synthetic X-ray AGN catalogs should be useful for interpreting additional trends (e.g. environmental dependencies) and as a helpful tool for quantifying AGN contamination in galaxy group and cluster X-ray surveys.