I'm currently a first year medical student, but I have a bachelor of science in marketing and am also interested in incorporating a master's level business education into my background. I must tell you that credentials only take you so far in the business world (different than academia where it's all about credentials). By this I mean, if you want to work for a bio-tech company and use your science background (M.D/D.O)...well then it really dosen't matter which masters you receive...although without a doubt the MBA is the most prestigous in the business world and is the most widely known. In a scientific role, you'll only need a modest business background, if any, because you are there to act as a "translator" between medical and business practioners (medical/ surgical sales, drug rep, etc). However, if you plan on running a hospital or doing something more business oriented, you must realize that you will be out matched if you don't have proven business experience (simply saying "I'm an MHA, MBA, MMM.....but I have no actual business experience" won't land you these non-science based business positons just like having an M.D. with little experience won't qualify you to become the head of a dept or chief of staff).
My humble opinion:
-Define goals......what do you want to do with your degree?
(If you want non-healthcare/science administration, I would get some real world experience first because business executives tend to talk about how physicians tend to be terrible at business and how they tend to be difficult to work with....offset this false generalization with practicle and tangible experience).
-Realize that an MHA and MMM lock you into the medical profession (generally speaking) so if you pursue these specialized degrees, be sure that this is the role that you would be happy with.
-once you have defined a goal...get the most specialized degree you can in that area. If healthcare, get an MBA in healthcare management (or MHA, MMM...I'd go with the MBA though as the MMM/MHA tend to be more clinically oriented - ex. chief of staff) and gain real world experience in these fields. If non healthcare/science, definitly get the MBA as opposed to the MHA/MMM degrees and specialize from there (IT, project management, finance, etc)....and if you're not sure what you want to do or want to leave yourself the option to change fields...get a general MBA.
-Lastly, do what makes YOU happy!
Sorry that was long, but I hope It helped. Good luck in the future!