Before revision: The 3-phase machines have major advantages of the single-phase ones: the power is constant (the power consumption of the single-phase motor varies over the cycle); smaller size (and thus lower cost) for the same power; the transmission over 3 wires need only 3/4 of metal for the wires that would be required for a two-wire single-phase transmission line for the same power; better power factor.
After revision: The 3-phase machines have major advantages of steady state torque is constant, leading to less vibration and longer service life (the instantanous torque of a single-phase motor pulsates with the cycle)the single-phase ones: the power is constant (the power consumption of the single-phase motor varies over the cycle); smaller size (and thus lower cost) for the same power; the transmission over 3 wires need only 3/4 of metal for the wires that would be required for a two-wire single-phase transmission line for the same power; better power factor.