Ok, it's the undergraduate programme known as BIEM (bachelor in international economics and management), right? Basically, BIEM is focused on management, while BIEF is more focused on finance and eventually economics, since you can choose a "pure" economics major (not sure if it's possible at BIEM too). In general, at BIEM you will find people more interested in management (practical subject of how to manage companies, not focused on math or traditional economics), while BIEF is more a mix, with many people there genuinely interested in economics (and the hard math that comes with it). Anyways, the first semesters are very very similar as course content, and then you can switch course.
I'm not sure what "business economics" means exactly, here at Bocconi we have these "international" areas: economics, finance, management, computer science (which to my knowledge includes tech management and quantitative economics), government (from an economic perspective).
BIEM/BIEF are the older international courses, so they are well known and organised, teaching quality in my opinion is good, but depends heavily on the subject and the professor (my management course was very well taught, mathematics well, microeconomics not, but attendance was useless anyways for the exam).
If you have any specific question feel free to ask!