The prevailing structural paradigm for the aqueous electron is that of an s-like ground-state wave function that inhabits a quasi-spherical solvent cavity, a viewpoint that is supported by numerous atomistic simulations using various one-electron pseudopotential models. This conceptual picture has recently been challenged, however, on the basis of results obtained from a new electron-water pseudopotential model that predicts a more delocalized wave function and no well-defined solvent cavity. Here, we examine this new model in comparison to two alternative, cavity-forming pseudopotential models. We find that the cavity-forming models are far more consistent with the experimental data for the electron's radius of gyration, optical absorption spectrum, and vertical electron binding energy. Calculations of the absorption spectrum using time-dependent density functional theory are in quantitative or semiquantitative agreement with experiment when the solvent geometries are obtained from the cavity-forming pseudopotential models, but differ markedly from experiment when geometries that do not form a cavity are used.