We present a generalization of the self-consistent analysis of carbon nanotube (CNT) field effect transistors (FETs) to the case of multi-wall/multi-band coherent carrier transport. The contribution to charge diffusion, due to different walls and sub-bands of a multi-wall (mw) CNT is shown to be non-negligible, especially for high applied external voltages and 'large' diameters. The transmission line formalism is used in order to solve the Schrödinger equation for carrier propagation, coupled to the Poisson equation describing the spatial voltage distribution throughout the device. We provide detailed numerical results for semiconducting mw-nanotubes of different diameters and lengths, such as current-voltage characteristics and frequency responses.