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 aggregate demand and supply), we can observe different demand structures. Do they have an impact on the auction efficiency and revenue-raising properties? It is essential to understand better the impact of competition structure on performance in order to draw recommendations for the design of multi-unit auctions. Theoretical results demonstrate on a simple case contrasting 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, that there are multiple equilibria leading to different performance outcome. Experiments are conducted to compare the performance of these two auctions. Results support that with a constant competition degree, the seller gets higher expected revenue with a lower variance when he faces a large number of bidders with small individual demands. We show that this result is attained with no significant effect on allocative efficiency.