That's an excellent question and I understand your confusion. I don't know how much info I can give considering that I have no MBA/PhD experience. What I can tell you, however, is that an MPH with a concentration in health admin will probably not give you enough exposure to the business of medicine, especially if you are business oriented. This is because, although I'm sure the programs vary among schools, an MPH is a broad degree that often madates exposure to all aspects of PH (health behavior/ policy/ biostats/ epidemiology/ environmental health). Therefore you lose time to those core courses.
Many of my health admin professors at UAlbany School of Public Health were PhDs in other fields. Additionally, students pursuing an MBA at my school were permitted to cross register with our health admin courses. I am unsure of what you are specifically looking for, but if you are considering a rigorous health-business exposure, go with the MBA and cross register for health-admin courses. Of course you would be postponing med school for a year or more of med school and you could lose the "med school groove", so that might be the tougher option.
Many of my core courses were math or science-related (ie. anything with the prefix "bio" in it). The science courses are cake since they are often presented to students with no previous science exposure. Everything in health admin was business related (I even took Strategic Management, the apex of most business programs). It took me 2 full years to complete the degree, including 2 6-credit internships (1 in the summer and one in my last semester).
I am happy with my degree mostly because a large percentage of my class were already physicians and I knew I wouldn't have to eventually go back to school for it! Physicians are notoriously awful managers and I feel that I have an edge over other medical gradutes due to my understanding of health care organization and delivery. We can't risk losing more money when we're trying to pay off our huge debts.
Good luck with your search for more info and of course call schools for advice.
Will