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We use hydrodynamical cosmological simulations to test the differences between cold and self-interacting dark matter models (CDM and SIDM) in the mass range of massive galaxies ($10^{12}M_{\odot}h^{-1}<M<10^{13.5}M_{\odot}h^{-1}$). We consider two SIDM models: one with constant cross section $σ/m_χ=1\mathrm{cm^2g^{-1}}$ and one where the cross section is velocity-dependent. We analyse the halo density profiles and concentrations, comparing the predictions of dark-matter-only and hydrodynamical simulations in all scenarios. We calculate the best-fit Einasto profiles and compare the resulting parameters with previous studies and define the best-fit concentration-mass relations. We find that the inclusion of baryons reduces the differences between different dark matter models with respect to the DM-only case. In SIDM hydro runs, deviations from the CDM density profiles weakly depend on mass: the most massive systems ($M>10^{13}M_{\odot}h^{-1}$) show cored profiles, while the least massive ones ($M<10^{12.5}M_{\odot}h^{-1}$) have cuspier profiles. Finally, we compare the predictions of our simulations to observational results, by looking at the dark matter fractions and the distribution of strong lensing Einstein radii. We find that in SIDM the DM-fractions decrease more rapidly with increasing stellar mass than in CDM, leading to lower fractions at $M_{*}>10^{11}M_{\odot}$, a distinctive signature of SIDM. At the same time, the distribution of Einstein radii, derived from both CDM and SIDM hydro runs, is comparable to observed samples of strong lenses with $M>10^{13}M_{\odot}h^{-1}$. We conclude that the interplay between self-interaction and baryons can greatly reduce the expected differences between CDM and SIDM models at this mass scale, and that techniques able to separate the dark and luminous mass in the inner regions of galaxies are needed to constrain self-interactions.