We use the Copernicus Complexio (COCO) high resolution $N$-body simulations to investigate differences in the properties of small-scale structures in the standard cold dark matter (CDM) model and in a model with a cutoff in the initial power spectrum of density fluctuations consistent with both a thermally produced warm dark matter (WDM) particle or a sterile neutrino with mass 7 keV and leptogenesis parameter $L_6=8.7$. The latter corresponds to the coldest model with this sterile neutrino mass compatible with the identification of the recently detected 3.5 keV X-ray line as resulting from particle decay. CDM and WDM predict very different number densities of subhaloes with mass $leq 10^9,h^{-1},M_odot$ although they predict similar, nearly universal, normalised subhalo radial density distributions. Haloes and subhaloes in both models have cuspy NFW profiles, but WDM subhaloes below the cutoff scale in the power spectrum (corresponding to maximum circular velocities $V_{mathrm{max}}^{z=0} leq50~mathrm{kms}^{-1}$) are less concentrated than their CDM counterparts. We make predictions for observable properties using the GALFORM semi-analytic model of galaxy formation. Both models predict Milky Way satellite luminosity functions consistent with observations, although the WDM model predicts fewer very faint satellites. This model, however, predicts slightly more UV bright galaxies at redshift $z>7$ than CDM, but both are consistent with observations. Gravitational lensing offers the best prospect of distinguishing between the models.
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