We present an analysis of a suite of simulations run with different particle- and grid-based cosmological hydrodynamical codes and compare them with observational data of the Milky Way. This is the first study to make comparisons of properties of galaxies simulated with particle- and grid-based codes. Our analysis indicates that there is broad agreement between these different modelling techniques. We study the velocity dispersion-age relation for disc stars at z= 0 and find that four of the simulations are more consistent with observations by Holmberg, Nordstroem & Andersen in which the stellar disc appears to undergo continual/secular heating. Two other simulations are in better agreement with the Quillen & Garnett observations that suggest 'saturation' in the heating profile for young stars in the disc. None of the simulations has thin discs as old as that of the Milky Way. We also analyse the kinematics of disc stars at the time of their birth for different epochs in the galaxies' evolution and find that in some simulations old stars are born cold within the disc and are subsequently heated, while other simulations possess old stellar populations which are born relatively hot. The models which are in better agreement with observations of the Milky Way's stellar disc undergo significantly lower minor-merger/assembly activity after the last major merger, that is, once the disc has formed. All of the simulations are significantly 'hotter' than the Milky Way disc; on top of the effects of mergers, we find a 'floor' in the dispersion that is related to the underlying treatment of the heating and cooling of the interstellar medium, and the low density threshold which such codes use for star formation. This finding has important implications for all studies of disc heating that use hydrodynamical codes.