Hey! Northeastern student here:
What I think @proudterrier is talking about with “personality” is that the two schools, while having many similarities, more and more these days, can attract very different students. Generally speaking, you’ll get more of an LAC in the city feel with BU, while Northeastern is a more technical and professionally oriented school with the co-op program and its strengths in Business and STEM. Northeastern will be known well in industry, the northeast, and many technical fields while BU will be more known in academia across many subjects. Of course, both are known in the reverse as well, but this is the “primary” way the schools are viewed. Northeastern also used to be a technical commuter school, who has invested a ton in changing to a more traditional residential college, and improving more of their academic programs. Some is window dressing done for rankings, but there are a lot of big tangible changes as well, from facilities to faculty hiring and more programs being offered and invested in. BU was seen as the stronger school academically for some time historically, though they are more peers now.
I will say this: Northeastern’s “personality” certainly has changed, but it will always have the co-op program as its centerpiece, which has defined the school for over a hundred years. I think part of the reason Northeastern has risen and become so popular is because a big part of the reality of education today is that how it works to set up your career is important. Not everyone can afford the luxury of education for the sake of education, which is why the conversation of college selection has shifted a bit.
BU and Northeastern students do share a few bonds: both laughing when BC claims to be “in Boston”, a strong hockey rivalry (This is where personality shows. BU students chant “SAFETY SCHOOL” at Northeastern, who chants back “WE HAVE JOBS”), and in generally are very friendly with each other. As a general student, you won’t interact too much with the other school, but it isn’t uncommon to have friends at the other. I have a few from a past internship myself 
To answer the original question in the title, absolutely BU is a great school with plenty of opportunities. In respect to Northeastern, the difference really comes down to fit, not quality. Both are great schools, depending on what you want to do.