First off Congrats on your acceptances and scholarship offers those are some impressive schools.
With that said realize that I or anyone else on anonymous internet poster board knows anything about you or your situation, and is certainly not capable of knowing what choice is best for you. What anonymous internet posters like myself can offer our some factors to consider when choosing a law school.
With that said I think any potential 0L should consider the following factors in this order when choosing a law school (1) Location; (2) Cost; (3) Personal Feelings about the School; (4) Understanding the reality of legal education; (5) last and least U.S. News and employment stats
I will analyze each factor to your particular situation and do with my anonymous internet poster advice what you will.
I do not know where you are from, if you have friends in Chicago or Durham N.C, but your personal situation in regards to location is something to consider.
Additionally, as you likely know Chicago and Durham North Carolina are very different places, but many law students including myself when I was a 0L do not fully grasp the importance of where their law school is located. You will be spending three years of the prime of your life in Chicago or Durham North Carolina. What it really comes down to is are you someone that wants to spend their prime in a big City or a College town. I personally love College towns and Duke Basketball and think North Carolina has a more laid-back pace, which I enjoy.
However, I am not you maybe you are someone that woudl love going to Wrigley Field, Museums, Plays, etc and there is no right or wrong answer, but do realize law school does not exist in a vacuum and the City you attend law school in will have a major impact on your life.
On top of that odds are you will end up in the state or at least nearby where you attend law school. If you want to be a Federal Clerk in Chicago the Federal Judges in Chicago are more often than not U of Chicago Alumni and will hire locally. In the Carolina's many Federal Judges are Duke Alumni and will hire Duke Alumni. You will also likely take the NC Bar Exam if you attend Duke and the Illinois Bar Exam if you attend Chicago.
On top of that during your three year law school career you will make friends, get an apartment or house you like, enter into a serious romantic relationship, etc and it will be very difficult to leave somewhere you have spent three years of your life. Of course there are exceptions, but the odds are if you attend Chicago you will end up living in Chicago and if you attend Duke you will end up in the South. Both are fine, but really ask yourself where you want to be. (2) Cost
Duke 49k (tuition)
Living Expenses (17K)
66k x 3 years = $198,000 - 90k scholarship= $98,000 debt
Chicago 47k (tuition)
Living Expenses (22k)
69k x 3 years= $207,000 - 45k scholarship = $162,000 debt
That is assuming you keep the scholarship years 2 and 3 of course. One thing to really watch out for are the scholarship conditions. Often it will be something along the lines of maintaining a 3.0 GPA or finishing in the top 50% of the class. I am sure that sounds like a piece of cake to someone who is being offered scholarships to these schools, and you probably could have obtained a 3.0 in undergrad without even trying, but law school is much different. 100% of students are smart, hard-working, and motivated and truly believe they will finish in the top 10%, but 90% won't. In regards to the 3.0 many schools have a stiff curve that allows only 35% of first year students to have a 3.0 GPA, which means in that scenario there is a 65% chance you will lose your scholarship for years two and three.
This New York Times Article does a better job of explaining the situation than I can. http://www.nytimes.com/2011/05/01/business/law-school-grants.html?pagewanted=all&_r=0
With that said I encourage you to negotiate for more money from these schools and carefully read the conditions and negotiate for better ones. If both of these schools are offering you scholarship money you have a lot of bargaining power and you should use it, once you enroll it is gone. (3) Personal Feelings About the School:
Your post indicated some thought to this in that you thought U of Chicago would be more competitive. I do not know if that is true or not, but I do know that each school has a culture to it and whether a school is the right fit for you personally is a decision only you can make. I strongly encourage you to visit both U(Chicago) and Duke talk to professors, admins, students, walk around the campus, walk around the neighborhood, and see what feels right. I am sure one will leave you with a better feeling than the other and you should really listen to that feeling. (4) Reality of Legal Education:
No matter what ABA law school you attend you will receive a quality education, and you will learn the same exact thing at any school. Your first year will consist of Torts, Civil Procedure, Contracts, Property, and LRW. In these courses you will read Supreme Court Cases and the Supreme Court does not write separate opinions for different schools. In Torts you will read the Palsgraf case to learn Proximate Cause, Civil Procedure Pennoyer v. Neff, Contracts Hadley v. Baxendale so on and so on. You will also learn how to cite cases and statutes in LRW.
At the end of your three years at Duke or Chicago you will sign up for either Barbri or Kaplan to help you pass the bar exam and study your ass off with students from schools all over the world. Then on the day of the bar exam you will be crammed into a room with a bunch of very nervous and stressed out recent law graduates taking the bar exam. If you pass that exam you are a licensed lawyer if not you are not a lawyer.
(5) U.S. News and Stats:
U.S. News is a for profit unregulated magazine offering an opinion and both Duke and UChicago were well regarded schools long before this magazine existed and will be well regarded if and when U.S. News stop publishing. As a tiebreaker use U.S. News, but nothing more since odds are by time you graduate these schools will have likely changed positions and one will be higher than the other at the time of graduation.
Employment Stats again these are fine to look at, but they do not really mean anything. Simply because 90% of people at X school pass the bar exam does not mean you can slack off or that a job will be handed to you. 10% of that 90% didn't pass or find a job etc. Stats are nice to look, but the reality is whether you succeed in the legal profession or not will have far more to do with you as an individual than the school you attended. Conclusion:
I know when I was a 0L I wanted someone to tell me X school was the right choice, but no "right" choice exists. Both of these schools are amazing and will offer you an abundance of opportunities, but no matter, which school you choose your life will change and to some extent you will always wonder "what if' I chose the other one. I really think your best bet is to visit each school and really ask yourself if you want to live in a College town or Big City all other things considered are more less equal.
Good luck in your decision and congrats on your acceptances.