Arts Administration and Museum Studies programs are really what you make of it, which was appealing to me. As my cohort and I begin out thesis this summer, we have a really wide variety of topics. Yes, there are a lot of business-y ones like membership programs, fundraising and governmental support for the arts, but theres also some curatorial thesis topics, and education. Mine will be about how museum educators can use different types of technology to teach. As Fullofpink says, there are a lot of administrative courses (which at times i dislike) but if I ever want to run an education department, i sure better know how a multi-million-dollar budget works, etc.
If you go the Museum/Administration route, see how long the program is. A 2 year program has intro classes the first year and a sub-specialization the second year, whereas the one year programs are *very* general. Also, be aware that a Masters in Art History will not get you too far in museum curatorship. Curators and their assistants also have phds. Now, if you would want to curate something like a residency program or be an independent curator, the masters would be enough.
Part of this, you must also remember is who wants you, meaning, what are your past experiences? Have you ever worked in a gallery? That might land you a spot in an Arts Admin program. Have you assisted with an exhibition catalogue? that might get you into art history.