Is it better for a seller who wants to auction multiple units to face many small bidders or few large bidders? Since multi-unit auction models usually have many equilibria, there are no theoretical predictions on the impact of the competition structure on the performance of a multi-unit auction (in terms of expected revenue and allocation efficiency). Our experimental results with uniform-price auctions support that with a constant degree of rationing, when the number of bidders increases while individual demand decreases, there is less strategic bidding (demand reduction). It leads to higher expected revenue with a lower variance but allocation efficiency is not significantly different