The gamma-ray emission from Starburst and Star-forming Galaxies (SBGs and SFGs) strongly suggests a correlation between star-forming activity and gamma-ray luminosity. However, the very nature of cosmic ray (CR) transport and the degree of their confinement within SBG cores are still open questions. We aim at probing the imprints left by CR transport on gamma-ray and neutrino observations of point-like SFGs and SBGs, looking into quantitative ways to discriminate among different transport models. We analyse the 10-yr Fermi-LAT spectral energy distributions of 13 nearby galaxies with two different CR transport models, taking into account the corresponding IR and UV observations. We also generate mock gamma-ray data to simulate the CTA performance in detecting these sources. In this way, we propose a test to discriminate between the two CR models, quantifying the statistical confidence at which one model can be preferred over the other. We point out that the current data already give a slight preference to CR models that are dominated by advection. Moreover, we show that CTA will allow us to firmly disfavour models dominated by diffusion over self-induced turbulence, compared to advection-dominated models, with Bayes factors, which can be as large as 10(7) for some of the SBGs. Finally, we estimate the diffuse gamma-ray and neutrino fluxes of SFGs and SBGs, showing that they can explain 25 per cent of the diffuse HESE data while remaining consistent with gamma-ray limits on non-blazar sources.