To date, two detailed ionic models of human atrial cell electrophysiology have been developed, the Nygren et al. model (NM) and the Courtemanche et al. model (CM). Although both models draw from similar experimental data, they have vastly different properties. This paper provides the first systematic analysis and comparison of the dynamics of these models in spatially extended systems including one-dimensional cables and rings, two-dimensional sheets, and a realistic three-dimensional human atrial geometry. We observe that, as in single cells, the CM adapts to rate changes primarily by changes in action potential duration (APD) and morphology, while for the NM rate changes affect resting membrane potential (RMP) more than APD. The models also exhibit different memory properties as assessed through S1-S2 APD and conduction velocity (CV) restitution curves with different S1 cycle lengths. Reentrant wave dynamics also differ, with the NM exhibiting stable, non-breaking spirals and the CM exhibiting frequent transient wave breaks. The realistic atrial geometry modifies dynamics in some cases through drift, transient pinning, and breakup. Previously proposed modifications to represent atrial fibrillation-remodeled electrophysiology produce altered dynamics, including reduced rate adaptation and memory for both models and conversion to stable reentry for the CM. Furthermore, proposed variations to the NM to reproduce action potentials more closely resembling those of the CM do not substantially alter the underlying dynamics of the model, so that tissue simulations using these modifications still behave more like the unmodified NM. Finally, interchanging the transmembrane current formulations of the two models suggests that currents contribute more strongly to RMP and CV, intracellular calcium dynamics primarily determine reentrant wave dynamics, and both are important in APD restitution and memory in these models. This finding implies that the formulation of intracellular calcium processes is as important to producing realistic models as transmembrane currents.