If two species have similar niches (similar resources in a given environment), then you would expect the two species to have an overlap of competing against the same resources. Thus, the resource would be limited.
What you are thinking is probably realized niche, where the organism would have to incorporate with the other organism in a similar niche. In that way, it would still be divergent just because it is coming from an ancestral, and the environment changes their beak size perhaps if they were competing against different seed size.