Cosmological hydrodynamical simulations are rich tools to understand the build-up of stellar mass and angular momentum in galaxies, but require some level of calibration to observations. We compare predictions at z ∼ 0 from the EAGLE, HYDRANGEA, HORIZON-AGN, and MAGNETICUM simulations with integral field spectroscopic (IFS) data from the SAMI (Sydney-AAO Multi-object Integral field spectrograph) Galaxy Survey, ATLAS3D, CALIFA (Calar Alto Legacy Integral Field Area), and MASSIVE surveys. The main goal of this work is to simultaneously compare structural, dynamical, and stellar population measurements in order to identify key areas of success and tension. We have taken great care to ensure that our simulated measurement methods match the observational methods as closely as possible, and we construct samples that match the observed stellar mass distribution for the combined IFS sample. We find that the EAGLE and HYDRANGEA simulations reproduce many galaxy relations but with some offsets at high stellar masses. There are moderate mismatches in Re (+), e (-), s e (-), and mean stellar age (+), where a plus sign indicates that quantities are too high on average, and minus sign too low. The HORIZON-AGN simulations qualitatively reproduce several galaxy relations, but there are a number of properties where we find a quantitative offset to observations. Massive galaxies are better matched to observations than galaxies at low and intermediate masses. Overall, we find mismatches in Re (+), e (-), s e (-), and (V/s)e (-). MAGNETICUM matches observations well: this is the only simulation where we find ellipticities typical for disc galaxies, but there are moderate differences in s e (-), (V/s)e (-), and mean stellar age (+). Our comparison between simulations and observational data has highlighted several areas for improvement, such as the need for improved modelling resulting in a better vertical disc structure, yet our results demonstrate the vast improvement of cosmological simulations in recent years.