Before I am accused of being biased, I'll agree with Mikell Taylor: both schools are power hitters in EE/CS. Even though I am one of those "MechE folks," I know the general atmosphere of the EE/CS department (Course VI) at MIT and it is definitely intense. (They have a t-shirt that says "Six Hertz" on the front and "Six Bytes" on the back...probably comments people made while somewhere between the 10th and 11th hours of their problem set.) The first few required courses cover general electromagnetic theory, circuitry, and "basic" CS, which isn't that basic at all IMHO. You can then choose between EE/CS with an EE focus, a CS spin, or somewhere in between. I suspect it's similar at Stanford.
Of course, we didn't win Darpa...I know we have a team, but I don't know if they actually entered a vehicle.
Also, have you looked into CMU (not the camera)? Any list of top CS schools includes them.
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MIT Mechanical Engineering
>> College Mentor,
Team 97: Cambridge Rindge and Latin School with The Edgerton Center, MIT Mechanical Engineering, Bluefin Robotics, and Draper Laboratory
>> Alumnus, Team 527: Plainedge HS