I was accepted to both schools, and chose to go to Duke (so I am biased). However, I live in Palo Alto (where Stanford is) and have a lot of friends that go there.
First off, Duke has a better soccer program and the most athletically minded student body of any school out there.
Second, Duke and Stanford are really similar schools. They both offer great educations and sports programs, have enthusiastic and involved student bodies, and beautiful campuses. At either you will be able to have a good social life, as both have a pretty big party scene and greek system.
The biggest separating aspect between them is the surrounding area. Duke is situated in Durham, NC while Stanford is in Palo Alto, CA. North Carolina is a lot different than California, I'd say the pace of life is slower and culture is more important to people. Furthermore Palo Alto is a lot nicer and safer city than Durham, although there is definitely fun to be had in both. In Palo Alto, the weather is more temperate, which can be good or bad. Its definitely nice in the winter. You never need much more than a hoodie and jeans whereas it snows in NC. However, in palo alto you will not get the seasons. North Carolina has amazing fall and spring seasons. Overall, the surrounding area by Stanford is nicer with more things to do, plus its in California.
If you are looking down the road, it depends what you want to major in. Both are extremely highly regarded as far as academics go. Biology, Engineering, Economics - Duke is more highly regarded. For pretty much everything else - Stanford. Both has some of the most involved alumni of any university, and can give you incredible networking and career opportunities.
If you still can't decide from this, go visit them.
I know six or seven guys on the Duke soccer team, they all love it and are a really tight-knit group (as i assume is the same at stanford).
P.S. The Duke UNC rivalry is something unlike anything else.
I go to Duke, but live 3 minutes from Stanford and was accepted there.