This is coming not from a perspective student but just someone who is interested in knowing what the difference is between each of the elusive Ivy League colleges. They are all unique because they are difference schools. This answer could come from the popular clubs, majors, what the students are like, the reputation of the school etc.
prospective*
A simple google search will yield you tons of results on this.
I suggest you read the Fiske Guide to Colleges (my favorite) and perhaps also Princeton Review and the Insiders Guide.
Almost any such taxonomy will be so reductive as to approach meaninglessness.
Dartmouth: outdoorsy, athletic, not usually the read-poetry-for-fun type. Gregarious…enjoy parties & beer.
Brown: suspicious of tradition and authority, therefore liberal politically, enjoy the lack of required classes … Kind of sheltered…not forced outside comfort zone by views or subjects they dislike.
Penn: diverse students with fondness for city life. More prone to being dedicated to a certain profession (biz, engineering, nursing etc) than other Ivies.
Cornell: sort of like Penn except replace fondness with urban life with being ok with remote location. Gets grief from those at other ivies (who care about such things) for being bigger, easier to get into, and younger than other ivies.
Columbia: urban, liberal, fast paced. Least athletic of Ivies.
Princeton: intellectual upper -crust country club atmosphere.
Yale. leaning left, inclined towards “softer” fields like law, acting, history English, philosophy.
Harvard: money, quite impressed with selves. Innovative.
(just as I anticipated…)
Regarding #4, #5 and #6
For better or worse, Life magazine felt comfortable with a similar approach: