Just to supplement this observation for those who do not know . . .
Memorial Quadrangle is Branford College on three sides, and Saybrook College on the fourth, which are two of Yale’s residential colleges (and really it is Branford turf–Saybrook’s courtyards are on the other side).
It actually has a somewhat interesting history–when it was first built with funding from Anna Harkness, the residential college plan was still in the future, and it was originally used for College seniors. Edward Harkness then gave the donation that really kicked off the residential college system, the complex was modified a bit, and it was converted into the separated Branford and Saybrook.
In that sense it is a very foundational space for Yale’s transformation into a Collegiate Gothic college modeled on Oxford, and indeed other colleges that followed a similar path after Yale (although Yale was not itself remotely first in the US).
However, it is not really a space frequently visited by the public or indeed other Yale students, it is instead mostly used by Branfordians.
Old Campus in contrast is a mix of some first-year housing, some academic buildings, and some other College buildings. So lots of College students spend lots of time on Old Campus, particularly as first years but also for various classes, events, and so on.