They have several differences, which is what have kept them from harmonizing. ISO 13485 is a standard based on ISO 9001 that is specific to medical devices. This standard is not adopted by the Food and Drug Administration (FDA) but the FDA participated in writing ISO 13485 to make sure their requirements and ISO 13485 are aligned. The FDA QSR has more stringent complaint handling & reporting requirements
However, if a company meets the requirements of ISO 13485:2003, they should easily be able to meet the FDA Quality System Requirements (QSR).