  In this work, we compare the SMBH and host galaxy properties of X-ray
obscured and unobscured AGN. For that purpose, we use $\sim 35 000$ X-ray
detected AGN in the 4XMM-DR11 catalogue for which there are available
measurements for their X-ray spectral parameters, from the XMM2Athena Horizon
2020 European project. We calculate the host galaxy properties via SED fitting
analysis. Our final sample consists of 1 443 AGN. In the first part of our
analysis, we use different N$_H$ thresholds (10$^{23}$ cm$^{-2}$ or 10$^{22}$
cm$^{-2}$), taking also into account the uncertainties associated with the
N$_H$ measurements, to classify these sources into obscured and unobscured. We
find that obscured AGN tend to live in more massive systems that have lower SFR
compared to their unobscured counterparts. However, only the difference in
stellar mass, M$_*$, appears statistically significant ($>2\sigma$). The
results do not depend on the N$_H$ threshold used to classify AGN. The
differences in M$_*$ and SFR are not statistically significant for luminous AGN
($\rm log (L_{X,2-10 KeV}/erg s^{-1})> 44$). Our findings also show that
unobscured AGN have, on average, higher specific black hole accretion rates
compared to their obscured counterparts. In the second part of our analysis, we
cross-match the 1 443 X-ray AGN with the SDSS DR16 quasar catalogue to obtain
information on the SMBH properties of our sources. This results in 271 type 1
AGN, at $\rm z<1.9$. Our findings show that type 1 AGN with increased N$_H$
($>10^{22}$ cm$^{-2}$) tend to have higher M$_{BH}$ compared to AGN with lower
N$_H$ values, at similar M$_*$. The M$_{BH}$/M$_*$ ratio remains consistent for
N$_H$ values below 10$^{22}$ cm$^{-2}$, but it exhibits signs of an increase at
higher N$_H$ values. Finally, we detect a correlation between $\Gamma$ and
Eddington ratio, but only for type 1 sources with N$_H<10^{22}$ cm$^{-2}$.
