Power range. Starting torque. Availability. Price.
If more than one or two kW, three phase is usually preferred. Starting torque for a single phase motor is usually low, fans need low starting torque. Single phase motors are not available for high kW applications. Price starts getting high in comparison when kW gets above a few kW.
120V 3-phase is extremely rare, 600V 3-phase is mostly Canadian. 208V 3-phase (200V motors) and 480V 3-phase (460V motors) are far more common in the US.
As long as I know, you should choose the higher voltage available on site. This is simply a matter of decreasing the current in the motor, meaning smaller and cheaper wires.