How is Nikon's PF optics different from and similar to Canon's DO optics?

Nikon has just announced a new 300 mm lens featuring a new technology called "PF" or "Phase Fresnel." This has been compared to Canon's existing DO (Diffractive Optics) lenses such as the 400 mm f4 DO. Both technologies are intended to allow creating shorter and lighter lenses, but how are the PF and DO technologies/optical elements different and similar? Is there any clear advantage to one or the other?