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The gamma-ray emission from Starburst and Starforming Galaxies (SBGs and SFGs) strongly suggest 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. Moreover, following the reported scenarios, we quantitatively assess the SBGs and SFGs contribution to the Extra-galactic Gamma-Ray Background (EGB data) and the IceCube diffuse observations (HESE data). We analyse the 10-year 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 generate mock gamma-ray data to simulate the CTA performance in detecting these sources. In the 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 current data already give a slight preference to CR models which are dominated by advection in their nucleus. 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 $25\%$ of the diffuse HESE data, while remaining consistent with gamma-ray limits on non-blazar sources.