Yeah I was in a similar situation. I also had a three-year undergrad (the new Bologna system; I assume that you, as an engineering student, had about 4 years instead of 5 as it used to be) and was also told that we should get a masters. Just FYI, it does count! I researched this myself, I emailed Harvard and asked them about it. The undergrad cycle, although shorter in Europe, is equivalent to the undergrad cycle in the US.
The MiM program is pretty decent, but yeah it depends which school you go to. Some are more prestigious than others. The thing what makes me shy away from the MiM is that it's pretty general. For me at least, since I already had an economics degree, it didn't make sense to go to a general program. For you maybe it's more worth your time, since you haven't had economics before.
I've also heard about the finance program at Bocconi. And yeah, Bocconi is pretty much the best-known school in Italy, so it's a really good thing to have on your CV. That's a better choice than the MiM, I feel, since it's more specialized in one direction instead of making you learn about the small, general things...
But here's some food for thought: you're Italian and you already have an Italian degree. Have you considered other options as well? You'd get a boost if you were to get a degree from a different country! There are plenty of good programs out there, especially if you're pretty confident in your English ability. Well, of course, there's also the issue of funding, since living costs in Italy are on the cheaper side of stuff in Europe...