Granite and quartz surfaces are very durable and capable of lasting a long time, whilst marble is porous and should have a quality sealer to prevent staining. Granite and quartz are also both heat, scratch, chemical and stain resistant, whereas the minerals that compose marble are sensitive to certain chemical agents. However, marble is famous for its unique and beautiful veining, which has led to the term "marbling", widely considered as a description of quality in many natural products from paper to steak. Quartz, used in fabrication, is an engineered stone.
As such, it's hard to duplicate the veining and patterns you get from genuine marble or granite. However, it is available in a multitude of colours and styles for a unique, custom look.