For those with both degrees, I think you have to first make a distinction between those with clinical training and those who do not.
For those who never did a residency, maybe they never intended to train or had an epiphany during med school that led them down a different path, but this type of MD/MBA will add some degree of extra value in business situations that a non-MD may not offer, especially when interacting with clients who are not MD's. These people are businessmen first, second and third, with a "bonus" of pre-clinical MD training. Many healthcare clients are now expecting to see MD's on consulting teams, and they don't generally make the distinction between those with and those without a clinical background. The MD will (generally) make you more attractive to potential employers and clients in the healthcare sector.
For those with an MD and clinical training plus the MBA you have more opportunities for provider managment and the chance to blend a career of patient care and business activities (e.g., part time clinician, internal consultant for health care system, or work for McKinsey 11 months out of the year and attend on a medical service for one month per year, etc.). Also, some get the MBA much later in their career as a "career changer", with a previous clinical career in their past and aspirations to be on the business side after the MBA. This can make a very powerful combination, but these types are usually older (and wiser), don't have the time for a full-time MBA program (who has 2 years to spend after making money as an attending with house/car payments, etc?) and are less willing to take entry-level business jobs (the work schedule as a first-year management consultant can be rough).
For me, I am in the middle of a residency, so I am taking the training route. Not because I "want to keep options open", but because I really enjoy the clincal aspect of medicine. My hope is that a hybrid position as an attending with a good amount of protected time will be available to me down the road so I can indulge both my clinical and business interests in the provider space. Residency is too much of a pain in the ass to go through with no plans to ever practice again - you have to really love it to put up with the downside. In terms of the pedigree for an healthcare administrator, it seems like MD/MBA's with a clinical background are en vogue these days (seems like in the early 90's there was a push for pure business types to captain the ship).
I have to run tonight, but I can get more specific if you have more questions.
