Average and scatter of the relative difference of the sparsity of the GADGET-X (blue squares) and GADGET-MUSIC (yellow triangles) clusters with respect to that of their GIZMO-SIMBA counterparts for different sparsity configurations in the case of the full (filled markers) and relaxed (empty markers) samples at z = 0 (top panel) and 1 (bottom panel), respectively. The errorbars represent the standard deviations for each sparsity configuration, while the shaded areas correspond to 5% and 10% variation respectively.