It is well known that the primary solar wind energy dissipation mechanism in the Earth’s upper atmosphere is Joule heating. Two of the most commonly used physics-based Global Circulation Models (GCM) of the Earth’s upper atmosphere are the Global Ionosphere/ Thermosphere Model (GITM) and the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM). At the same time, a number of empirical formulations have been derived to provide estimates of Joule heating rates based on indices of solar and geomagnetic activity. In this paper, a comparison of the evolution of the globally-integrated Joule heating rates between the two GCMs and various empirical formulations is performed during the solar storm of 17 March 2015. It is found that all empirical formulations on average underestimate Joule heating rates compared to both GITM and TIE-GCM, whereas TIE-GCM calculates lower heating rates compared to GITM. It is also found that Joule heating is primarily correlated with the auroral electrojet in GITM, whereas Joule heating in TIE-GCM is correlated better with the Dst index and with prolonged southward turnings of the Interplanetary Magnetic Field component, Bz. By calculating the heating rates separately in the northern and southern hemispheres it is found that in GITM higher Joule heating rates are observed in the northern hemisphere, whereas in TIE-GCM higher Joule heating rates are observed in the southern hemisphere. The differences and similarities between the two global circulation models and the various empirical models are outlined and discussed.