We investigate the supercluster shape properties of the all-sky observed (Abell/ACO) and simulated (Virgo data) cluster catalogues using an approach based on differential geometry. We identify rich superclusters by applying the percolation algorithm to both observed and mock cluster populations, the latter being constructed following the observational selection of the Abell/ACO sample, extended out to zmax≤0.114. We apply a set of shape diagnostics in order to study the morphological features of superclusters with ≥8 cluster members. Our results demonstrate that filamentarity is the dominant supercluster shape feature. On comparing data and models, we show that the ΛCDM (ΩΛ=1-Ωm=0.7) model performs better than τCDM, which is excluded at a relatively high confidence level, in agreement with other recent large-scale structure studies.