In this paper we infer the mass composition of the ultra high energy cosmic rays (UHECRs) from measurements of Xmax distributions recorded at the Pierre Auger (2014) and Telescope Array (TA) (2016) Observatories, by fitting them with all possible combinations of Monte Carlo (MC) templates from a large set of primary species (p, He, C, N, O, Ne, Si and Fe), as predicted by EPOS-LHC, QGSJETII-04 and Sibyll 2.1 hadronic interaction models. We use the individual fractions of nuclei reconstructed from one experiment in each energy interval to build equivalent MC Xmax distributions, which we compare with the experimental Xmax distributions of the other experiment, applying different statistical tests of compatibility. The results obtained from both experiments confirm that the mass composition of the UHECRs is dominated (≳70%) by protons and He nuclei in the energy range investigated lgE(eV) = [17.8–19.3] (Auger) and lgE(eV) = [18.2–19.0] (TA). The indirect comparisons between the Xmax distributions recorded by the two experiments show that the degree of compatibility of the two datasets is good, even excellent in some high energy intervals, especially above the ankle (lgE(eV)∼18.7). However, our study reveals that, at low energies, further effort in data analysis is required in order to harmonize the results of the two experiments.