They are both in Pittsburgh and from my understanding equally good schools.
I guess one thing to really look at are the stipulations of the scholarship. If it is something like you must maintaina 3.0, be a little careful. Most incoming law students think they will get a 3.0 no problem, but when you go to law school everyone will be very smart, hardworking and motivated. This is relevant, because typically the law school curve only allows about 1/3 of the class to get a 3.0, which means if there is a 3.0 requirement there is a 66.6% chance you will not keep your scholarship for year two and three. This is nothing personal, but just the reality on the first day of class 100% of law students are sure they will be in the top 10% and there is no way they will not in at least the top third, but you do not have to be a math major to see how that plays out.
So one thing to do is review the stipulations of the scholarship.
Also, the culture of the school is important if you really liked Duquesne undergrad and did well there, why move? If you are eager to go to a bigger school then UPitt offers that. The actual legal education will be the same you will take Torts, Criminla Law, Civil Procedure etc at either school and typically when ABA schools are in the same city the same professor teaches at both schools. So I assume at either school you will have the same professor and read from the same textbook.
In summary there is no "right" choice, both schools will provide you with an opportunity to succeed. However, at the end of the day you will have to choose one and you will always wander what would happen if you choose differently, and you will simply never know, but it will likely end up fine.
If you want a little more reading material here is a great article on how to choose a law school. http://www.legalmatch.com/choose-the-right-law-school.html