You should not only match the motor to the power supply but you should match the equipment requirements to the lower motor speed. Specifically, it may not be enough to simply install a 50hz motor on the existing equipment that was designed for 60hz speeds.
For a hoist or conveyor, when changing changing the speed from 60hz to 50hz, the device will run at 83% of the original speed. The slower speed may or may not be be a problem depending on the customer requirements.
However, for a centrifugal compressor, pump, or fan, the flow will be reduced proportional to the reduction in speed so that the new flow will be 83% of the original flow. More importantly, the output pressure (or pump head) will be reduced proportion to the square of the reduction in speed so that the new pressure will be 69% of the original pressure. Depending on the application that the compressor, pump, or fan is used for, the reduction in flow and pressure may render the equipment inoperable.