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Various simulations of a GaN HEMT are used to study the behaviors of two different energy-transport models: the Fermi kinetics transport model and a hydrodynamics transport model as it is implemented in the device simulator Sentaurus from Synopsys. The electron transport and heat flow equations of the respective solvers are described in detail. The differences in the description of electron flux and the discretization methods are highlighted. Next, the transport models are applied to the same simulated device structure using identical meshes, boundary conditions, and material parameters. Static simulations show the numerical convergence of Fermi kinetics to be consistently quadratic or faster, whereas the hydrodynamic model is often sub-quadratic. Further comparisons of large signal transient simulations reveal the hydrodynamic model produces certain anomalous electron ensemble behaviors within the transistor structure. The fundamentally different electron dynamics produced by the two models suggest an underlying cause for their different numerical convergence characteristics.