From Quora
If you’re interested in doing really deep theoretical research in computer science, then Princeton might actually be a better fit for you. This is mainly due to Princeton’s long tradition of excellence in pure mathematical research and related areas (physics, theoretical CS, etc.) Princeton is home of the Institute for Advanced Study, which is where a lot of really brilliant CS theoreticians have crossed paths.
But if you’re interested in doing anything practical in computer science (i.e. anything that actually involves writing code) then Stanford is the best place to be, bar none. In general, the Ivy Leagues are not as good as Stanford when it comes to practical subjects.
This is not to that the Stanford’s CS Theory Group is shabby. Quite the contrary, Stanford has a very strong Theory Group in its own right and it’s still getting stronger. They hired Ryan Williams not too long ago, who made one of the biggest breakthroughs in complexity theory in the last decade.
But at the same time, my perception is that CS Theory kind of gets overshadowed at Stanford by everything else that’s going on there. Very few people at Stanford are content to just stand in-front of a whiteboard all day. Both the students and the professors are involved in start-ups. Rajeev Motwani and Jeff Ullman advised the Google founders, when they were PhD students, and they were both high profile Theory faculty members at Stanford.
So I’d say that Stanford and Princeton are very different cultures.
At Princeton, you can be working on an arcane problem that may not be solved in your lifetime, and people will cheer you on. You can be playing with little oddities like John Conway’s Game of Life, and people will be impressed.
At Stanford, if you’re really smart and talented, people will expect that you’re working on the next Google.