We present a comprehensive study of the star formation histories of massive-quenched galaxies at z = 3 in three semi-analytical models (SHARK, GAEA, GALFORM) and three cosmological hydrodynamical simulations (EAGLE, ILLUSTRISTNG, SIMBA). We study the predicted number density and stellar mass function of massive-quenched galaxies, their formation and quenching time-scales and star formation properties of their progenitors. Predictions are disparate in all these diagnostics, for instance: (i) some simulations reproduce the observed number density of very massive-quenched galaxies (> 10(11) M-circle dot) but underpredict the high density of intermediate-mass ones, while others fit well the lower masses but underpredict the higher ones; (ii) in most simulations, except for GAEA and EAGLE, most massive-quenched galaxies had starburst periods, with the most intense ones happening at 4 < z < 5; however, only in SHARK and ILLUSTRISTNG we do find a large number of progenitors with star formation rates > 300 M-circle dot yr(-1); (iii) quenching time-scales are in the range approximate to 20-150 Myr depending on the simulation; among other differences. These disparate predictions can be tied to the adopted active galactic nucleus (AGN) feedback model. For instance, the explicit black hole (BH) mass dependence to trigger the 'radio mode' in ILLUSTRISTNG and SIMBA makes it difficult to produce quenched galaxies with intermediate stellar masses, also leading to higher baryon collapse efficiencies (approximate to 15-30 per cent); while the strong bolometric luminosity dependence of the AGN outflow rate in GAEA leads to BHs of modest mass quenching galaxies. Current observations are unable to distinguish between these different predictions due to the small sample sizes. However, these predictions are testable with current facilities and upcoming observations, allowing a 'true physics experiment' to be carried out.