Identification of high-redshift X-ray active galactic nuclei in the 4XMM-DR11 serendipitous catalogue using DES data Comparative analysis with optically selected QSOs

X-rays provide a robust method in identifying active galactic nuclei (AGN). However, in the high-redshift Universe (z >= 3.0), their space density is relatively low and due to the small areas covered by X-ray surveys, the selected AGN are poorly sampled. Deep optical and infrared (IR) data are essential for locating counterparts and determining redshifts. In this work, we leverage the XMM-Newton 4XMM-DR11 serendipitous catalogue (1240 deg(2)), alongside the extensive optical Dark Energy Survey (DES, 5000 deg2) and the near-IR VISTA Hemisphere Survey (VHS) to select one of the largest high-redshift X-ray AGN samples to date. Our analysis is focussed on the overlapping area of these surveys, covering about 185 deg(2). In addition, we aspire to compare the properties of the X-ray AGN with optically selected QSOs. For sources without spectroscopic data (similar to 80%), we estimated the photometric redshifts using both spectral energy distribution (SED) fitting and machine-learning algorithms. Among the similar to 65 000 X-ray sources in the 4XMM-DES-VHS area, we ended up with 833 z >= 3.5 AGN (11% having spec-z information) with a high level of reliability, along with a fraction of outliers of eta <= 10%. The sample completeness is similar to 90%, driven by the depth of DES data. Only similar to 10% of the X-ray selected AGN are also optical QSOs and vice versa. Our findings indicate an observed absorbed fraction (log NH [cm(-2)] >= 23) of 20-40% for the X-ray AGN, significantly higher than that of optical QSOs. X-ray AGN exhibit fainter observed optical magnitudes and brighter mid-IR magnitudes than optical QSOs. Their median rest-frame SED shapes differ notably with optical QSOs being dominated by AGN emission in the UV-optical wavelengths. While the median SEDs of X-ray AGN suggest extinction in the UV-optical range, individual sources exhibit a wide range of spectral shapes, indicating significant diversity within the population. This analysis supports the notion that X-ray-selected and optically selected AGN represent distinct and complementary populations.