I have several friends at NYU, and the word is that all of the 'on paper' stuff is the same. Very similar course requirements (mostly taking first year courses together), very similar degree requirements, very similar stipends. I have no idea about admissions; Stern has a smaller class, but that doesn't tell us anything about which is harder to get into.
Students in both departments have access to both departments' profs, if proactive. I would say the main distinction is whether you'd rather be in a class of 2-3 or a class of ~20 students.
If I'm not mistaken, one can apply to both.