IDK if I am qualified to answer as I attended RPI (undergrad) and NYU Engineering is the old Polytechnic University (grad) 25+ years ago. I have kept up some with what both schools are doing,etc.
At NYU Poly you major in Mech E with a minor in aerospace. So probably not the place to go if you want a great education in aero E. Also, since they have what I consider a regional reputation as a engineering school, NYU Poly probably does not have the name recognition as RPI or Case Western.
I disagree with the above statement that RPI does not have a strong co-op program. I knew of many classmates that participated years ago. Those that wanted to, can. Not everyone wanted to take a semester off, especially since graduating engineers were getting job offers without co-op experience. My roommate had no interest because she had great summer positions and on-campus research opportunities and was planning to go to grad school. Another arranged found his own job in the area and turned it into a co-op (company signs some papers, he filled out his report, etc.). Another found a summer opportunity in Switzerland. I did what they now call ‘parallel co-op’ - I worked full time in the Albany area and took 2 courses at night at RPI. So not everyone needs to participate in the formal co-op program (semester off and Summer).
I think it is best to visit both schools (RPI and Case Western) during their accepted students days to see which one feels like the best school for you.