Squeaking:

Rubber makes no noticeable sound while polyurethane has the possibility of squeaking (if not properly lubricated).

Most common complaints about poly bushings is that they squeak where rubber bushings do not. While it is true that poly can squeak it is usually a result of the part not being properly lubricated during install, as all poly bushing manufactures recommend and sometimes require to avoid warranty issues.

Rubber does not squeak since the bushing is chemically bonded to the metal shell and sleeve. The torque of suspension movement is soaked up by the bushing internally so the rubber does not move against the metal, and thus, no noise (although this does contribute to the wear of the bushing).