Pressurized thin-wall structures cover a broad range of applications, including storage tanks, pressurized rubber flood barriers, and large span enclosures. To accurately model such structures, the analyst must select the appropriate mechanical formulation (e.g. membrane vs shell). Membranes are assumed to have negligible bending stiffness and respond to compression by wrinkling; shells resist axial compression (before buckling) and bending efficiently. While theoretical research on these differences is vast, this study aims to explicitly clarify the consequences of this choice and permit a comparison of error between membrane and shell formulations. Therefore, this paper presents a parametric study of canonical pressurized thin-wall structural geometries (i.e. semi-cylinder, hemisphere) to illustrate the transitions between membrane and bending dominant behavior. The mathematical models of a pneumatic 5-parameter shell and membrane are presented and employed to quantify the effects of variables such as thickness and geometry on the amount of membrane, bending, and shear energy. The effects of inflation pressure, self-weight, and hydrostatic loads are also considered. The graphical results, presented in terms of dimensionless quantities in the design space, are general and should be of interest to the theorist and practitioner alike.