i'd definately say edinburgh, its a much more pleasant city to live in than leeds, the buildings are beautiful and the city does have a hell of a lot of shops, tell her to check out princes street (about a mile long street outside waverley station). edinburgh also has a good clubbing scene but has the added advantage of the finge festival in the summer too. edinburgh is a much more cultural place (big café culture, lots of museums and art galleries) and its got lower crime rates than leeds, which in some areas can be really rough (one of my friends who's at leeds met got mugged outside her flat).
although edinburgh is a more expensive city to live, its generally regarded as one of the best places in the country to live, it was once voted best place to live in the world. by all means leeds is a great student city too, but it hasn't got a patch on edinburgh. edinburgh is one of those places you go to and feel sad to leave, i instantly felt at home their.
of course, these are only my opinions, best thing to do is that your friends goes and visits them both to see which she likes best.