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In this study, our primary objective is to compare the properties of SMBH andtheir host galaxies between type 1 and type 2 AGN. In our analysis, we useX-ray detected sources in two fields, namely the eFEDS and the COSMOS-Legacy.To classify the X-ray sources, we perform SED fitting analysis, using theCIGALE code. Ensuring the robustness of our analysis is paramount, and toachieve this, we impose stringent selection criteria. Thus, only sources withextensive photometric data across the optical, near- and mid-infrared part ofthe spectrum and reliable host galaxy properties and classifications wereincluded. The final sample consists of 3,312 AGN, of which 3\,049 areclassified as type 1 and 263 as type 2. The sources span a redshift range of$\rm 0.5<z<3.5$ and encompass a wide range of L$_X$, falling within $\rm42<log,[L_{X,2-10keV}(ergs^{-1})]<46$. Our results show that type 2 AGN exhibita tendency to inhabit more massive galaxies, by $0.2-0.3$\,dex, compared totype 1 sources. Type 2 AGN also display, on average, lower specific black holeaccretion rates, a proxy of the Eddington ratio, compared to type 1 AGN. Thesedifferences persist across all redshifts and L$_X$ considered within ourdataset. Moreover, our analysis uncovers, that type 2 sources tend to havelower star-formation rates compared to 1 AGN, at $\rm z<1$. This picturereverses at $\rm z>2$ and $\rm log,[L_{X,2-10keV}(ergs^{-1})]>44$. Similarpatterns emerge when we categorize AGN based on their X-ray obscuration levels($N_H$). However, in this case, the observed differences are pronounced onlyfor low-to-intermediate L$_X$ AGN and are also sensitive to the $\rm N_H$threshold applied for the AGN classification. These comprehensive findingsenhance our understanding of the intricate relationships governing AGN typesand their host galaxy properties across diverse cosmic epochs and luminosityregimes.

The properties of supermassive black holes and their host galaxies for type 1 and 2 AGN in the eFEDS and COSMOS fields