I interviewed at both places and believe they are both great programs, you cant really go wrong here. Both have very nice facilities, good faculty, many clinical rotation sites, lottery system for clinical years, and good match lists. I think the biggest differences between the 2 schools are location/climate, type of campus, tuition, and reputation. CCOM is in Chicagos suburbs (Midwest, cold winters, etc.), its a small graduate-student campus, tuition&fees are ~$55k, and has a well-established reputation (+100 years old with a large alumni network ie. lots of connections that you may benefit from). NSU is right outside of Fort Lauderdale (South Florida, warm weather, etc.), its a large University campus with lots of resources (gym, libraries, etc.), tuion&fees are ~$46k, and NSU has been around for a while but isnt as recognized as CCOM. Which of these differences mean the most to you? Are either close to your hometown with family/friends/support network? There are some minor differences in the schools like CCOM doesnt record lectures, CCOM has the sweetest anatomy lab ever, NSU has a dress code and required rural rotation, the NSU dean has an awesome mustache
but none of those factors would of swayed me one way or another.
A couple other things to mention
If you take a look at their match lists, the majority of students that match into Anesthesiology at both schools match into ACGME programs. Im not sure how dead set you are on that specialty, but every med student Ive talked to has said you will change your mind multiple times during school, so dont let that be a decision factor for you.
CCOMs rotation sites are supposed to be excellent and are all in the greater Chicago area. While Im not sure about the quality of NSUs sites, they are spread out throughout South Florida, other parts of the state, and a few in neighboring states. If you are looking to not be bounced around during clinical years, CCOM may be the better choice.
Hope some of that helps, good luck with your decision!