In this work we compare the generalized Fulton-Gouterman transformation (GFGT) and the Lee-Low-Pines transformation (LLPT). We apply both to a general electron-phonon Hamiltonian including the Frohlich Hamiltonian, an electronic periodic potential, phononic anharmonicities, and Umklapp processes. We respectively discuss the ability of the two unitary transformations to achieve approximate electronic diagonalization in general and also for a particular electronic Bloch base. We further consider their possible application to multiparticle systems. It turns out that in general the GFGT is a more successful technique than the LLPT.