In this paper, we examine the theoretical foundations of the quantum drift-diffusion and density-gradient transport models for the simulation of fully-depleted silicon-on-insulator and silicon nanowire FETs. In doing so, we highlight the strengths and limitations of both approaches. In the former case, the harmonization of the classical and quantum-mechanical perspectives is pursued by means of Bohm’s theory of quantum potential and by solving, in addition to the coupled Schrödinger–Poisson equations, as many drift-diffusion equations as the number of populated subbands. The latter approach is affected instead by more serious conceptual problems, as it basically replaces the Schrödinger equation with a simplified non-linear equation in the electron-charge concentration, by which energy quantization, multiple subbands, and multiple effective-masses are neglected. Despite these limitations, the density-gradient model turns out to be remarkably successful in predicting the device I– V characteristics. Simulation examples are discussed and the model predictions are compared. In our implementation, the simulation efficiency of the QDD is superior to that of the DG model.