I actually see NYU more like Manchester.
For one, they are both very large institutions.
Manchester too is very selective in certain fields it has strengths in like Physics, Mathemetics, Computer Science and Engineering. In most of the other fields, it is just above average/quite good and less selective.
Also, just like NYU, Manchester produces some high quality alumni, Nobel Laurettes and does very well in most international rankings, sometimes better than members of the Golden Traingle (for Manchester)/Ivy Plus (for NYU), yet they both struggle to be seen in the same light as these universities because of their size.
They are just not seen as highly selective enough and don’t ooze prestige when mentioned. There are many brilliant students studying in them and many just above average students as well, as they have a lot of bums to fill.