Context. Barium (Ba) stars are polluted by material enriched in the slow neutron capture (s-process) elements synthesised in the interior of their former asymptotic giant branch (AGB) companion star, which is now a white dwarf. Aims. We aim to compare individual Ba star abundance patterns to AGB nucleosynthesis model predictions to verify if the AGB model mass is compatible with independently derived AGB mass, which was previously estimated using binary parameters and Gaia parallax data. Methods. We selected a sample of 28 Ba stars for which both self-consistent spectroscopic observation and analysis were performed and, additionally, stellar mass determinations, via positioning the star on the Hertzsprung-Russell (HR) diagram and comparing with evolutionary tracks are available. For this sample of stars, we considered both previously (Y, Zr, Ce, and Nd) and recently derived (Rb, Sr, Nb, Mo, Ru, La, Sm, and Eu) elemental abundances. Then, we performed a detailed comparison of these s-process elemental abundances to different AGB nucleosynthesis models from the Monash and the FRUITY theoretical data sets. We simplified the binary mass transfer by calculating dilution factors to match the [Ce/Fe] value of each star when using different AGB nucleosynthesis models, and we then compared the diluted model abundances to the complete Ba-star abundance pattern. Results. Our comparison confirms that low-mass (with initial masses roughly in the range 2-3 M·), non-rotating AGB stellar models with 13C as the main neutron source are the polluters of the vast majority of the considered Ba stars. Out of the 28 stars, in 21 cases the models are in good agreement with both the determined abundances and the independently derived AGB mass, although in 16 cases higher observed abundances of Nb, Ru, Mo, and/or Nd, Sm than predicted were present. For three stars, we obtain a match to the abundances only by considering models with masses lower than those independently determined. Finally, four stars show much higher first s-process peak abundance values than the model predictions, which may represent the signature of a physical (e.g. mixing) and/or nucleosynthetic process that is not represented in the set of models considered here.