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We test cosmological hydrodynamical simulations of galaxy formation regarding the properties of the Blue Cloud (BC), Green Valley (GV) and Red Sequence (RS), as measured on the 4000$\small{ \mathring {\mathrm A}}$ break strength vs stellar mass plane at $z=0.1$. We analyse the RefL0100N1504 run of EAGLE and the TNG100 run of IllustrisTNG project, by comparing them with the Sloan Digital Sky Survey, while taking into account selection bias. Our analysis focuses on the GV, within stellar mass $\log\,\mathrm{M_\star/M_{\odot}} \simeq 10-11$, selected from the bimodal distribution of galaxies on the D$_n$(4000) vs stellar mass plane, following Angthopo et al. methodology. Both simulations match the fraction of AGN in the green-valley. However, they over-produce quiescent GV galaxies with respect to observations, with IllustrisTNG yielding a higher fraction of quiescent GV galaxies than EAGLE. In both, GV galaxies have older luminosity-weighted ages with respect to the SDSS, while a better match is found for mass-weighted ages. We find EAGLE GV galaxies quench their star formation early, but undergo later episodes of star formation, matching observations. In contrast, IllustrisTNG GV galaxies have a more extended SFH, and quench more effectively at later cosmic times, producing the excess of quenched galaxies in GV compared with SDSS, based on the 4000$\small{ \mathring {\mathrm A}}$ break strength. These results suggest the AGN feedback subgrid physics, more specifically, the threshold halo mass for black hole input and the black hole seed mass, could be the primary cause of the over-production of quiescent galaxies found with respect to the observational constraints.