Yikes. A true dilemma I see. I just googled the MSIA and see that it's a one-year MBA; it's just not called one. I'm not sure if I'd be interested in doing a one-year accelerated MBA and then pursuing another MBA for the sake of having an MBA. If the MBA's what you're after, go for it. After all, it's marketable in all sectors. However, I must say that one-year isn't bad especially if your current objective is develop your managerial skills and still have access to academia and all it's bells and whistles like internships, jobs and exchange programs which WILL NOT be readily available when you exit.
FYI I declined a full ride at Carnegie Mellon for a master's in policy and management because I didn't want the curriculum. I probably would have really considered it if it wasn't a two year program but it was so I nixed it because I'm adamant about attending b-school (no interest in policy whatsoever). Go with the environment and curriculum in which you are most interested and most likely to thrive (intellectually, professionally, personally, etc).