At first I thought this question was the typical DDS vs DMD. I think a Graduate Diploma of Dentistry would either refer to an international diploma that certifies people to practice dentistry (based on the structure of their education) OR a researcher type degree in the US (like a master's in oral biology). I'm not really sure.
If you want to be a full on dentist in the US then you need a DDS/DMD, and in that case there is no difference between the two.