Raw engine power!

Note that the propeller on the [XF-84H Thunderscreech][1] did move at supersonic speed. There is nothing inherent in propellers which prevents their tips from moving faster than the speed of sound.

On the other hand, the big diameter of a prop requires proportionally more torque to keep the prop rotating against the drag from the supersonic tips. Thus, a fan engine requires less torque to reach supersonic tip speeds on the fan blades.

Also, the [shroud of a turbofan engine helps a lot][2] to make the noise from supersonic tips manageable. The XF-84H's noise made people literally sick.

Generally, a fully subsonic fan would be more efficient. But then the diameter would need to be as large as that of big turboprop engines, and the shroud would become impossibly heavy and produce too much drag. The high dynamic pressure on the fan blades is needed to produce the thrust with the relatively small diameter of a turbofan.

  [1]: http://aviation.stackexchange.com/questions/21683/did-the-xf-84h-thunderscreech-really-cause-900-sonic-booms-per-minute/21700?s=1%7C0.1966#21700
  [2]: http://aviation.stackexchange.com/questions/11884/do-nacelles-around-aircraft-engines-help-in-reducing-the-engine-sound/11891#11891