I just have to throw into the mix my perception as a student outside of both IL and TX. I guess these comments are based more on reputation than actual knowledge about details of these programs that might set them apart.
Baylor has a national reputation and many of my classmates have applied there. Rush and UIC do not have a national reputation and I do not know anyone who is applying there, even amongst people who are considering other programs in Chicago and the midwest.
I too have heard rumors about Methodist taking some of the better Baylor faculty when they broke off to form their own residency programs (affiliated with Cornell, of all places). People applying for surgical residencies specifically told me that the best faculty left for Methodist, whereas IM applicants I have met on the interview trail gave the more vague report that Baylor is "rebuilding." Regardless, at Baylor you end up training at amazing institutions like Texas Heart Institute and Ben Taub (the County hospital), with access to the rest of the Texas Medical Center. The Baylor name is recognized as a center of medical excellence, even if the program may be a bit in flux at the moment.
In short, I never would have considered this grouping of programs to be in the same league. I suppose if one were interested in specifically staying around Chicago, then Rush might be worth pursuing, but if having to decide between Baylor and Rush without that sort of geographic bias, I would not hesitate whatsoever to choose Baylor.