Currently trying to make the same decision. From what I've gathered, Stanford is stronger in optics, MIT is stronger in devices/materials. Most electronic materials based research at Stanford seemed to be graphene/2D, while MIT offered a wider interpretation of what electronic materials could consist of.
Trying to choose between Stanford and MIT for EE PhD program. I like the faculty and interdisciplinary vibe of Stanford, but I'd prefer to stay on the east coast. Is MIT really as cutthroat as people say it is? The social environment is pretty important to me. Also nervous about how many people make it past quals...