We use nonadiabatic mixed quantum/classical molecular dynamics to simulate recent time-resolved photoelectron spectroscopy (TRPES) experiments on the hydrated electron, and compare the results for both a cavity and a noncavity simulation model to experiment. We find that cavity-model hydrated electrons show an "adiabatic" relaxation mechanism, with ground-state cooling that is fast on the time scale of the internal conversion, a feature that is in contrast to the TRPES experiments. A noncavity hydrated electron model, however, displays a "nonadiabatic" relaxation mechanism, with rapid internal conversion followed by slower ground-state cooling, in good qualitative agreement with experiment. We also show that the experimentally observed early time red shift and loss of anisotropy of the excited-state TRPES peak are consistent with hydrated electron models with homogeneously broadened absorption spectra, but not with those with inhomogeneously broadened absorption spectra. Finally, we find that a decreasing photoionization cross section upon cooling causes the excited state TRPES peak to decay faster than the underlying radiationless relaxation process, so that the experimentally observed 60-75 fs peak decay corresponds to an actual excited-state lifetime of the hydrated electron that is more likely similar to 100 fs.