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Competition in a multi-unit auction is measured, both by the number of bidders, and by the relative size of their demands compared to the number of units on sale. For the same degree of competition (identical supply and aggregate demand), we can observe different demand structures. Do these have an impact on auction efficiency and revenue-raising properties? It is essential to better understand the impact of competition structure on the performance of multi-unit auctions so as to be able to make recommendations for their design. In a simple case that compares a uniform-price auction of two bidders with a demand of 6 units each and an auction of 6 bidders with a demand of two units each, theoretical results show that there are multiple equilibria leading to different performance outcomes. Experiments are conducted to compare the performance of these two auctions. Results indicate that, with a constant degree of competition, the seller obtains higher expected revenue with a lower variance when they face a large number of bidders with small individual demands. We show that this result is obtained with no significant effect on allocative efficiency. Classification JEL: C92 ; D4 ; D44.