I'm not sure I agree with the analogy for MIT/Stanford as an _institution_ (in terms of the curriculum, administration's goals, etc.), but I definitely think it's true for the students and overall atmosphere.
Blowing things up and hacking on random projects :is to: MIT students ||
Starting a new business :is to: Stanford students
MIT folks also often use the word "Sloanie" (referring to someone in the business school) as a fairly derogatory term. (Though I guess this is a common view in general).