Yale is, of course, older and most likley has more alumni in high places than NYU does. It is also a more well known name in higher education world-wide and its alumni network is huge and diverse in terms of areas of expertise. There are opportunities for engagement with alumni across disciplines in many places around the world, if you are so inclined. It also has more athletics if you are ever inclined to go to a college football or hockey game.
New Haven is relatively compact and accessible yet it is feasible to live off campus and have a car. This is far less economically feasible in NYC yet, in some ways, less necessary as public transportation is ubiquitous.
In terms of education, both schools have good reputations. NYU roses in the rankings originally due to a huge influx of federal cash after Superstorm Sandy (Oct 2012) which wiped out some of NYU's infrastructure (Bellevue, the nearby public hospital, was evaculated and had no patients for the first time since it opened in 1736.) The philanthropy that made it possible to go tuition-free further increased the school's ability to attract the best and the brightest although it remains to be seen what they will do with that education.
The Yale System in terms of exams, grades and original research has been in place for decades. It has been a cradle for medical education leadership for decades, often as a pipeline to Boston and out to the rest of the country.
Go to the place that feels right for you... some will thrive in the highrise jungle of Kips Bay and others will prefer The Green, the Sound, and the Hill.
