James Donovan and Carol Watson (2012) tackle this question by looking at whether placing an article in an institutional repository hurts its ranking in a disciplinary repository. The authors argue that readers are not a zero-sum game, and so more readers for an article in one repository does not necessitate fewer readers for the same article in another repository.
Instead, different kinds of readers go to different kinds of repositories for different reasons. For example, a small but very interested group of readers will receive table of content alerts from the Social Science Research Network (SSRN). Other readers may have less interest in the subject area as a whole, and so will not have subscribed to alerts from a traditional repository. Instead, they want information from the article at a point of need, and arrive through a keyword search from Google. (Organ (2006) found that 95.8% of the downloads in their institutional repository came through Google). Donovan and Watson point out that institutional repositories are often listed in the first few Google results, while SSRN pages are listed later. This can be a crucial difference when readers may not go beyond the first page or two of search results. In addition, in two case studies, Donovan and Watson found that institutional repository readers tended to arrive in a steadier stream than the first group of readers, who peaked shortly after the article was announced in SSRN.
Thus, the argument is made that having an article in one repository does not hurt its ranking in another: more copies and more access points means more readers for the article.
For more information on institutional repositories, and other forms of self-archiving, look at eprints FAQs: http://www.eprints.org/openaccess/self-faq/
Donovan, J. M., & Watson, C. A. (2012). Will an institutional repository hurt my SSRN ranking?: Calming the faculty fear. AALL Spectrum, 16(6), 12-13.
Organ, M. K. (2006). Download statistics-what do they tell us? The example of research online, the open access institutional repository at the University of Wollongong, Australia. Academic Services Division-Papers, 44.