NYU Shanghai is being touted as the first/only Sino-Foreign cooperative higher education institution in the media lately, though it isn't -- there are literally hundred of joint programs, ranging from dual-degree programs to genuinely independent institutions jointly managed by Chinese and foreign entities (e.g., Xi'An Jiaotong Liverpool University, University of Nottingham Ningbo, United International College, SIAS International University, and others).
NYU, though, is the highest-profile American university to start a program, and is following what you might call the Nottingham model, where the foreign university essentially dictates the entire curriculum (aside from P.E. and Marxist thought, one assumes -- traditionally required courses for all Chinese university students).
So while it isn't the only or first university to start such a program, it is possibly the biggest, highest-ranked (#43 on the QS Rankings!), most prestigious (just the words "New York" command attention), and most PR-savvy. A lot of people will be watching to see how it succeeds or fails. A number of facets of this institution will probably be under scrutiny: academic freedom, success of graduates in terms of employment or grad school admissions, treatment of language (English proficiency of local students, and, one hopes, Chinese proficiency of foreign students*), and so on. It will be really interesting to see what comes of this venture.
*I'm not yet clear on how these will be treated, but so far there does not appear to be a "first year English" program in place, which is mandatory at many other joint-venture universities.