Take this with a grain of salt because I know nothing about Northwestern other than what I've heard from other people. I've heard the two described as polar opposites in many ways; NW has a much different patient population (e.g., rich) than Chicago. NW is also located right in the heart of downtown, so you're in a much more flashy, glitzy area, which actually might be an advantage depending on how you look at it (I would imagine the cost of attendance would be much higher). The two communities the schools are in are very different.
Like any two schools, it really comes down to what you think. If you're interested in both schools, apply to both and see how things end up. Like I said, though, the rumor is that they're very different, and people who like one institution probably wouldn't like the other.
I know I am a newbie on this site, but I feel like I can contribute to th Pritzker vs Feinberg debate as it is currently consuming all of my brain power. I was accepted at both schools (and am currently deciding between the two- actually a VERY difficult decision). I agree that they are very different schools. Here's my two cents:
If you are unsure I would suggest applying to both. I actually didn't think I would like Northwestern because I though that they might be snobbish (I applied for undergrad- not the best experience). Regardless, I went to the interview day and they completely changed my perspective on the school. It was AMAZING. I figured I would really like UofC prior to the interview and lo and behold- it is still tied for my top choice. Granted, I didn't apply anywhere outside of the mid-west because I knew I wanted to be in Chicago.
Northwestern actually has a very diverse population of patients because they have a Level I Trauma center. A lot of patients come from all over the city because of this, so you see everyone from the rich and the fabulous to the indigent populations. So in this respect, there is a little something for everyone. I've toured their Prentice Hospital (the women's hospital), and as NickNaylor said it is pretty flashy (but I thought it was awesome!). UofC doesn't have the Level I Trauma, but they do have a lot of diversity and probably have better research facilities.
I would say that the biggest difference between the two schools is that Northwestern is more clinically oriented while UofC is more research oriented. For someone who likes to do both things (like me), this makes the choice between the two very difficult. Also, their teaching styles are quite different (PBL at NU, traditional lectures at UofC). In college I went to lecture and then studied the material in a group- thus this distinction between PBL and lecture is a wash for me. I learn both ways.
Location. Hyde Park has more of a neighborhood feel (brownstones, grass, TREES!), and Streeterville is all high rises and is 2 blocks from Michigan Ave near the Gold Coast (although the beach nearby is nice bonus feature).
The other thing to consider is reputation- I feel like UofC is more internationally known for research. A lot of the physicians I talk to in Chicago seem to think that going to UofC will land you a better residency, but in my opinion it's a wash between the two schools. Plus, you should rarely make a decision based on rankings and reputation, especially when the schools are so closely ranked.
As for cost of attendance, I believe that UofC is significantly more expensive than NU for the last 2 years (you should check my facts). I'll bet this makes up for the difference in cost of living. But like NickNaylor says, UofC is known for being generous with financial aid.
Hope this helps!