Every Stanford EE PhD I have spoken to (10-15) have said that the qual's reputation is no longer justified. If you fail the second time, but your advisor likes you, he can qualify you regardless of the test.
That said, the department is big and impersonal. It's extremely easy to work with non EECS advisors though.
I'm deciding between the same two schools, although not for Bioengineering (EE+Materials, instead). I haven't seen Tech yet, but my impression from Stanford is that there are virtually no boundaries on what you can count as EE research. They plug the fact that the EE building is across the street from the Medical center.
What are people's impressions of Atlanta? Palo Alto is not a good city for students...