I can't say from experience, as I'm actually only hoping to start my MPH this fall. However, if you consider what the study of Public Health is, you would probably answer your own question. You will be studying policy contextualized around health issues. Though the plus of an MPH versus an MPP is that an MPH has a nice balance between the social and natural sciences. You would have a better understanding of disease and health and clinical rhetoric. If you study for an MPP, on the other hand, you would just have a strong grasp on policy analysis and drafting, which can be applied to issues of the health of the public.
You said you wanted to study health disparities, so an MPH would allow you to really focalize on those disparities through a medical and sociological lens. An MPP would have you look at those disparities through the lens of politics and economy. I hope that helps?
Like I said, I haven't started my masters yet, but just having studied public health, it seems like the logical answer.