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8 Answers
Avneesh Singh Saluja
I did my undergrad at Stanford (albeit in the EE department) and am currently doing a PhD at CMU. My views:

CMU: there are very few universities around with such a CS emphasis across the board. You want to do NLP? There are a couple of guys at Stanford, an entire department at CMU. Same with robotics, HCI, machine learning, etc. I am truly impressed with the amount of resources that CMU dedicates to CS.

Stanford: no doubt, weather and location. Do not discount this factor, it becomes quite important!
Robert Frederking
Although I am faculty at CMU, I'd say the objective answer is to base this on the faculty and research groups in the specific area you are interested in.  The two schools don't have exactly the same research at the same time, and the most important thing in a PhD is the research.  You need to find a topic you're really excited about.  So, if you are fortunate enough to be accepted at both, spend significant time looking at the research groups in your area, and see which you are more in tune with.  BTW, the weather in Pittsburgh is fine in the summer, and you'll probably spend most of your summers here too while working on your PhD.
Justin Johnson
Both programs are fantastic - you really can't go wrong either way. That being said, one school or the other may be better fit for you depending on your specific research interests.

I had to make this decision last year, and it was a tough one. It might sound shallow, but in the end I chose Stanford mostly due to weather and location.