Hey, I was accepted to both Geffen and Drew and can give you some perspective on them.
Geffen = the regular 4 year MD program at UCLA. You do your 2 years and then rotate through all the UCLA affiliated Hospitals. Your degree comes from just UCLA.
Drew = 4 year program that focuses on the medically underserved. The idea is to train physicians who will want to practice in and serve underserved communities. You do the 2 pre-clinical years with the Geffen kids and then rotate at the UCLA hospitals that have a primarily underserved propulation (such as UCLA-Harbor) but you also have the option of rotating at the other UCLA affiliated hospitals as well. Drew students USED to do their rotations at MLK but the hospital lost its teaching accreditation. You also have to do a senior project (thesis) that focuses on the underserved to graduate. Your degree comes from both Drew and UCLA.
Prime = 5 year program that focuses on the medically underserved. You do the 4 year Geffen program and then take a fifth year to do an MBA, MPH, MA, etc.. that focuses somehow on the medically underserved. The idea is to train leaders in health policy, health economics, health disparities, etc.. that will go on to focus on underserved communities. I believe you might get some special funding for this fifth year (which I would be very attractive I would imagine).
Hope that helps!