they're not "harder", but they are different. If you're referring to gaining acceptance to an MBA or master's program versus med school (allo or DO), the med program is harder due to the monopoly on med programs -- 129 or so allo + some similar or smaller number of DO schools, versus 1000+ colleges or universities that offer MBA or master's programs. In my old city (Chicago) there were 2 top programs & probably 12 mid or lower tier ones, in that one city.
Top programs, at least on the business side, are seeking proven leaders who can manage and effect change, and have shown this in challenging corporate or business environments. That's what I mean by different -- take a look at some of the apps at the schools, at least the essay portion, and you'll get a feel for what they're looking for. Another indicator is average GPAs at schools -- look at Harvard MBA versus Harvard Med and you'll see, same at any top school; the best book-smart applicants are not what the business world is looking for.
Regarding applying MD/MBA, it varies -- I am aware of some programs in which you apply separately to each, or in which you apply first to one, and then to the other; some show preference for already-enrolled MDs, for example; I suspect this will wholly vary by school.
