Pros
Some of the brightest and best students and faculty on a global basis, so the inspirational value is high and there's a great sense of being at the leading edge of thought in many domains. The world outside shows great respect for a Harvard background. There is great freedom to structure your own time, but great pressure to perform without much detailed support re: how to get better. Harvard expects you to take the initiative.
Cons
The professional schools at Harvard focus less on contributing to the profession through the subsequent work of students, and more on published ideas of faculty as reviewed by other faculty around the globe. So, ultimately, this is faculty talking to faculty rather than staying closely connected to and influential with the world of practitioners. Too much faculty politics, too little real-world engagement, education, and career support.