Having worked closely with dozens of rush medical students over the years I can say with confidence that the students at Rush truly enjoy their program. Many of Rush's strengths have been articulated by others, but in my opinion they are worth repeating and dovetail with my own experiences and those of close friends and family members... strong focus on clinical medicine, nationally recognized specialty care (neurology, neurosurgery, orthopedics and geriatrics, come to mind), new hospital, wonderful community service opportunities, and rotations at Stroger/Cook County Hospital.
The Rush match list is on par with similar institutions across the country and in the Chicagoland area (Loyola and UIC). However, I believe comparing match lists is splitting hairs for the vast majority of future medical students.
Nationally, Rush has an excellent reputation among those practicing in areas related to Rush's strengths (a good, but imperfect guide is the US News and World Reports rankings/survey in which Rush does very well). Among the broader national community Rush is not as well known. Why? In part, it is where its alumni practice, a vast majority of Rush matriculants (75-80%) are Illinois residents and hence many stay put in Illinois after graduation. In addition, Rush does not have a large parent University (undergrad) which would serve to extend its name recognition nationally. All this being said, Rush students do practice and match all over the country, so don't let that deter you.
In short Rush students do seem to really enjoy the school but like all institutions Rush has its strengths and weaknesses.