AACSB is kind of the “gold standard” in business accreditation. There's others, but AACSB is the big one. I don't know Florida schools, so know that the FIU vs. NOVA piece means nothing to me, but AACSB vs IACBE, I'd pick AACSB, because it's going to have more “clout” behind it.
Now, if you're looking to work internationally, it could be that IACBE is more well-known in the international sphere; I don't know for sure. But, at least within the US, AACSB is much better known and more reputable.
However…despite having that be my starting point, I don't think you should be making a decision based on AACSB vs IACBE, or FIU vs NOVA. I think your decision should be 1st MBA vs MAcc, and then decide on a school and accreditation package that picks what you want and what you can afford. MBA and MAcc lead to different careers and brand you as a different type of candidate, so you need to figure out which career you want and which candidate you want to be before you pick one.
Personally, I want to go the private/management route, so MBA Finance is what I'm in the middle of (OK, so I'm only like 2 weeks into my first class, but that's middle…ish!). For the career route I want, CPA/MBA combo is the best option. MAcc wouldn't really help me as much. But, for a different career path, a MAcc might be preferable. (Oh, and at least in my MBA Finance curriculum, there's very little accounting – IIRC, only 1 accounting course.) Looking back at one of your prior posts (“2nd Bachelor in Accounting” thread), you talked about not wanting to be in management, but having jobs look for accounting credits; if your goal is to get accounting credits and not to work in an accounting management role, then I'd advise against the MBA route. MBA looks like “I want to run the department”; when paired with accounting coursework, CPA, etc., then it says “I want to run the accounting department”. If that's not what you want to say, then don't say it. 😛 But, if accounting courses are what you're lacking, the MBA won't provide them.
As far as the foundational courses, I'd say just take those prior to enrolling in a course. Don't pick a course based on those. Just enroll for a couple semesters taking a couple of those courses each semester as non-degree-seeking student so that you can learn the foundations. Taking them at a Master's price isn't necessary, as they'll probably be the same course as if you took them as a non-degree seeking student out of the undergrad catalog.