Among available quantitative magnetospheric models, the Tsyganenko models represent empirical modeling, while the Toffoletto and Hill model is theoretical analysis. By mapping flux tubes between the ionosphere and the magnetosphere, those two models are analyzed and compared. Both the implied and actual field-aligned currents (FAC) are calculated in both models. The implied FAC, required to maintain the model field in magnetostatic equilibrium and given by the Vasyliunas equation, has the same order of magnitude as observational data, even in non-equilibrium models. The actual FAC, given by Ampere's law, is much smaller than the implied FAC, which means no large extraneous FAC is included in those models. Several new approaches imply that none of these models are in magnetostatic equilibrium, while the discrepancies are considerably larger for the Tsyganenko models. The magnetic effects of a preliminary FAC model have been evaluated in the Toffoletto and Hill theoretical model.