Do you think you might want to go to Business or Law School? Having not spent any money for UG will make paying for that a lot easier.
Have you visited each school? UNC has a totally different feel than Stanford. I would strongly suggest a trip. And, as others have said a realistic assessment of the amount of debt that you are looking at. Congrats.
Any gains that you might get from the prestige factor would be more than nullified with your student loan payments. You’re exponentially better off taking the full ride at UNC for a lot of reasons. For instance, what if you get married? Your spouse might have 50k in student loans? If you have 75k in student loans, then you both have combined loans of 125k. What if you find out you hate your career and you want to go to graduate school? What if your kid has health problems? Life is going to happen whether you have high debt payments or not. The less debt the better 
@Pastpower, congrats again on a great run. Duke, Stanford, Brown, Carolina Honors… very impressive showing. I will add that when we visited Duke and UNC, got a much friendlier feel at UNC. Duke seemed a little intense. Also preferred the housing at UNC to the separated dorms at Duke for Freshman. In any case, if you pass on Stanford, you have a great opportunity in Raleigh. Go Tarheels!
Either school should provide you with ample opportunities. Here is a personal anecdote: I went to Stanford as an undergraduate, and I have a friend who went to his state flagship. We both did well in our respective institutions: I received various awards, including Phi Beta Kappa (given to the top 2% of each graduating class), while my friend was a Rhodes Scholar (a very prestigious scholarship to Oxford given to 32 graduates each year nationwide). We both ended up at the same medical school. So, we literally had different pathways to a similar outcome. An important consideration is to find a college environment where you can excel.
@Pastpower – have you decided?