CMU has an entire program dedicated to the specialty/similar areas, whereas UIUC has various faculty members across different labs dedicated to specialty. A second reason why CMU is still in the running is that if I enter the program I am making a commitment to a specialization (more or less), whereas in UIUC I would be able to play around in a few areas (which could be either positive or negative). Also, and perhaps it is just my perception, but I believe Carnegie Mellon is also a bit more prestigious. I am not sure whether this name recognition might be important in the future for PhD applications or for job placement.
Regarding the funding at CMU, I wasn't able to obtain real concrete stats, but based on some correspondence with grad students, it would seem that once they receive funding it is full funding. I unfortunately haven't been able to get much more than that. I have heard first hand accounts of students going, receiving full funding at the end of their first semesters, and not paying a dime for tuition, but I am sure there are stories on the other side as well.