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We use AGN with $\rm L_{X} \sim 10^{42.5-44}\,erg\,s^{-1}$, from the COSMOS-Legacy survey that lie within the UltraVISTA region and cross match them with the LEGA-C catalogue. The latter provides measurements of the calcium break, D$_n$4000, and H$_δ$ Balmer line that allow us to study the stellar populations of AGN and compare them with a galaxy reference catalogue. Our samples consist of 69 AGN and 2176 non-AGN systems, within $\rm 0.6<z<1.3$, that satisfy the same photometric selection criteria. We construct the SEDs of both population and use the CIGALE code to investigate the effect of the two indices in the SED fitting process. Our analysis shows that the inclusion of D$_n$4000 and H$_δ$ allows CIGALE to constrain better the ages of the stellar populations. Furthermore, we find an increase of the estimated stellar masses by, on average, $\sim 0.2$ dex, in particular for systems with young stars (D$_n$4000$\,<1.5$), when the two indices are included in the SED fitting. We then compare the D$_n$4000 and H$_δ$ of AGN with sources in the reference catalogue, accounting for the different stellar mass of the two populations. Low to moderate L$_X$ AGN tend to reside in galaxies with older stellar populations and are less likely to have experienced a recent star formation burst, compared to galaxies in the control sample. We, also, compare the two populations as a function of their morphology (bulge-dominated, BD, vs. non-BD) and compactness. A similar fraction of AGN and non-AGN systems are classified as non-BD ($\sim 70\%$). Our analysis shows that BD AGN tend to have younger stellar populations compared to BD, non-AGN systems. On the other hand, non-BD AGN have, on average, older stellar populations and are less likely to have experienced a burst compared to non-BD sources in the reference sample. Furthermore, AGN tend to prefer more compact systems compared to non-AGN.