Here we report on high field transport in GaN and GaN field effect devices, based on the rigid-ion model of the electron-phonon interaction within the Cellular Monte Carlo (CMC) approach. Using the rigid pseudo-ion method for the hexagonal wurzite structure, the anisotropic deformation potentials are derived from the electronic structure, the atomic pseudopotential, and the full phonon dispersion and eigenvectors for both acoustic and optical modes. Piezoelectric as well as anisotropic polar optical phonon scattering is accounted for as well. In terms of high field transport, the peak velocity is primarily determined by deformation potential scattering described through the rigid pseudo-ion model. The calculated velocity is compared with experimental data from pulsed I-V measurements. We simulate the effects of non-equilibrium hot phonons on the energy relaxation as well, using a detailed balance between emission and absorption during the simulation, and an anharmonic decay of LO phonons to acoustic phonons, as reported previously. Non-equilibrium phonons are shown to result in a significant degradation of the velocity field characteristics for high carrier densities, such as those encountered at the AlGaN/GaN interface due to polarization effects.