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Accounting for the triaxial shapes of galaxy clusters will become important in the context of upcoming cosmological surveys. We show that, compared to the gas density distribution, the cluster gravitational potential can be better characterised by a simple 3D model and is more robust against fluctuations. Perturbations in the gas density distribution can have a substantial influence on the derived thermodynamic properties, while cluster potentials are smooth and well-approximated by a spheroidal model. We use a statistical sample of 85 galaxy clusters from a large cosmological hydrodynamical simulation to investigate cluster shapes as a function of radius. In particular, we examine the shape of isodensity and isopotential shells and analyze how it is affected by the choice of component (gas vs. potential), substructure removal (for the gas density) and the definition of the computation domain (interior vs. shells). We find that the orientation and axis ratios of gas isodensity contours are degenerate with the presence of substructures and unstable against fluctuations. We observe that, as the derived cluster shape depends on the method used for removing the substructures, thermodynamic properties extracted from e.g. X-ray emissivity profiles suffer from this additional, often underestimated bias. In contrast, the shape reconstruction of the potential is largely unaffected by these factors and converges towards simple geometric models for both relaxed and dynamically active clusters. The observation that cluster potentials are better represented by simple geometrical models and reconstructed with a low level of systematics for both dynamically active and relaxed clusters suggests that by characterising galaxy clusters by their potential rather than by their mass, dynamically active and relaxed clusters could be combined in cosmological studies, improving statistics and lowering scatter.