This paper presents an axiomatic characterization of difference-form contests, that is, contests where agents' probability of victory depends on the difference of their effective efforts. This axiomatization rests on a pairwise comparison axiom that relates the winning probabilities of any pair of participants to their winning probabilities in a contest between the two of them. The resulting difference-form contest success function overcomes some of the drawbacks of the widely-used ratio-form. Contrary to other difference-form functions, the family we charaterize here can be scale invariant and have a positive elasticity of augmentation. By clarifying the properties of this family of contest success functions, this axiomatization can help researchers to find the functional form better suited to their application of interest.