If you study how two species of finches compete for food, are you dealing with community ecology, population ecology, organismal ecology, or ecosystem ecology?
You are dealing with community ecology.
Communities are defined as being all the living organisms (different species) that are found in a defined area. The species involved in your question are: bird species A, bird species B and whatever species of plants which produce the seeds or berries the finches are feeding on.
Organismal would be looking just at one species, population ecology would also look at one species.
Ecosystem ecology includes abiotic factors - this is not correct here since the two different species and the food they are competing for are all biotic factors.
Here is a video which discusses the levels of organization in ecology.