Context. Linking the star formation (SF) properties of dense clumps to their parent large-scale environment is a key step to interpret Galactic surveys. Achieving a consistent, multi-scale picture of SF requires a comparative analysis of observations and simulations. Aims. We exploit kiloparsec-scale magneto-hydrodynamic simulations designed to reproduce local Milky Way conditions. Leveraging the wide range of scales covered by the simulations (reaching a resolution of 0.03 pc), we aim to compare the properties of the simulated population of star-forming clumps with observational catalogues. Methods. After extracting the star-forming structures with the HOP clump-finding algorithm, we compare their physical (mass and size) and SF properties (SF rate and efficiency) with those of the Hi-GAL compact source catalogue. Results. Despite the different methodologies and the three-dimensional nature of our clump extraction, the simulated clumps show good agreement with the observed sample in their mass and size distributions. We discover a consistently linear relation between mass and SF rate (SFR) for the simulated clumps, which is remarkably independent of the initial conditions of the boxes. Using scaling relations to distinguish between turbulence- and gravity-regulated gas inflow onto the clump scales, we find tentative evidence in favour of a gravity-regulated regime of SF at the probed sub-parsec scales. Key words. methods: numerical - stars: formation - ISM: clouds