Loyola, Rush, and UIC are very comparable in terms of multiple factors. The faculty, patient population you will see, prep for boards, ability to achieve specialty of choice, etc. There are a few key differences:
1) Rush & Loyola, being private institutions, provide more "comfortable" conditions for their students. This means more free lunches, special lectures, possible better technology (or quicker to jump on), etc. For these things, you end up paying roughly 18k a year more in tuition.
2) Rush and & Loyola have smaller classes than UIC-Chicago, so probably a slightly better faculty to student ratio, for whatever that counts. Since so much training and attention goes into molding an MD, it may be that being at Rush (class size 140) might be better than being at UIC Chicago (class size ~200). Although UIC Rockford and UIC Peoria offer more intimate training with student N = ~60 per campus (with even more individual attention than Rush or LUC could provide).
3) Rush and UIC are involved in a lot of dedicated outreach work on the near west side of Chicago. Although Rush has a great community engagement office and global health program, in this regard I believe UIC's dedicated Urban med and Global med programs provide better and more formalized experience if those realms interest you.
4) Comparing Loyola and UIC-Chicago match numbers for 2017, you can see UIC has a slightly higher Primary care tilt, but specialist numbers are fairly comaporable. Additionally, Rockford and Peoria students typically score and match slightly higher on USMLE than UIC-Chicago:
UIC:
View attachment 230529
Loyola:
View attachment 230530
Long story short. Loyola and/or Rush end up costing about $80,000 in raw dollars more than UIC over the course of 4 years. If you are taking out loans, and ascribe to the rough 3:1 calculation. That ends up being $240,000 when you actually pay it all back by year 10 of being an attending.
In my opinion, $80,000, let alone $240,000 is not worth the marginally increased level of student comfort you may get at Rush/LUC vs UIC. All other factors are equal enough to balance out.