We compute the electron and hole mobilities in ultrathin body and buried oxide, fully depleted silicon on insulator devices with various high-k metal gate-stacks using nonequilibrium Green's functions (NEGF). We compare our results with experimental data at different back gate biases and temperatures. That way, we are able to deembed the different contributions to the carrier mobility in the films (phonons, front and back interface roughness, and remote Coulomb scattering). We discuss the role played by each mechanism in the front and back interface inversion regimes. We draw attention, in particular, to the clear enhancement of electron- and hole--phonons interactions in the films. These results show that FDSOI devices are a foremost tool to sort out the different scattering mechanisms in Si devices, and that NEGF can provide valuable inputs to technology computer aided design.