I don't know any numbers, but it seems as if Stack Exchange is far more popular, especially as an information database for employees and students.
Quora has the opportunity to do the same, but I think the specific stack exchange communities offer a better partition between topics. Quora does it's best to show you targetted questions/comments, whereas StackExchange sites just throw you wherever you showed up (which, if by search, is usually a better choice)
A good example : I once answered a fringe question about the Dalai Lama on Quora, now many of the questions i'm tasked with giving answers to are spiritual in nature, and of absolutely no interest to me. It's the same search bubble problem that YouTube/Google runs into occasionally. Things like that make me prefer more 'basic' sites like StackExchange networks.