Alien and native plant species often differ in functional traits. Trait differences could lead to niche differences that minimize competitive interactions and stabilize coexistence. However, trait differences could also translate into average fitness differences, leading to a competitive hierarchy that prevents coexistence. We tested whether trait differences between alien and native species translated into average fitness or stabilizing niche differences, and whether competition could explain observed coexistence within invaded grassland communities (New Zealand). Trait differences reflected marked competitive hierarchy, suggesting average fitness differences. Species coexistence was determined by a trade-off between species susceptibility to herbivory vs competitive hierarchy and facilitation. Importantly, although aliens and natives differed in their trait values, they did not differ in their competitive response, highlighting the importance of equalizing mechanisms in structuring invaded communities. Only a few alien species with a particular set of traits were able to jeopardize species coexistence when grazing was ceased. Our study explains why some alien species coexist with natives, whereas others have strong impacts on native communities. It highlights that trait differences can underlie several coexistence processes and that the demonstration of trait differences between aliens and natives is only a first step to understanding the role of biotic interactions in structuring invaded communities.