Competition between groups is ubiquitous in social and economic life, and groups are typically not created equal. Here we experimentally investigate the implications of this general observation on the unfolding of symmetric and asymmetric competition between groups that are either homogeneous or heterogeneous in the ability of their members to contribute to the success of the group. Our main finding is that, in contrast with a number of theoretical predictions, efforts in contests involving heterogeneous groups are higher than in contests involving only homogeneous groups, leading to reduced earnings (to contest participants) and increased inequality. This effect is particularly pronounced in asymmetric contests, where both homogeneous and heterogeneous groups increase their efforts. We find that asymmetry between groups changes the way group members condition their efforts on those of their peers. Implications for contest designers are discussed.