We compare subhalo mass and velocity functions obtained from different simulations with different subhalo finders among each other, and with predictions from the new semi-analytical model presented in Paper I. We find that subhalo mass functions (SHMFs) obtained using different subhalo finders agree with each other at the level of ∼20 per cent, but only at the low-mass end. At the massive end, subhalo finders that identify subhaloes based purely on density in configuration space dramatically underpredict the subhalo abundances by more than an order of magnitude. These problems are much less severe for subhalo velocity functions (SHVFs), indicating that they arise from issues related to assigning masses to the subhaloes, rather than from detecting them. Overall the predictions from the semi-analytical model are in excellent agreement with simulation results obtained using the more advanced subhalo finders that use information in six-dimensional phase-space. In particular, the model accurately reproduces the slope and host-mass-dependent normalization of both the subhalo mass and velocity functions. We find that the SHMFs and SHVFs have power-law slopes of 0.86 and 2.77, respectively, significantly shallower than what has been claimed in several studies in the literature.