Sometimes when we have recurring motifs (like the birds in R and J), it helps to think about who is speaking because it helps us understand more about them. It also helps to think of the nature of the birds each speaker describes
For Benvolio's part, any girl can be a bird; he speaks of Rosaline as a "swan" and a "crow", neither of which are particularly flattering, and both of which reveal something of Benvolio's attitude. Swans, though gracious and beautiful in appearance are mean; crows are even worse. Benvolio tells us that she will be unattractive in comparison, but he also reveals to us that in neither instance would she make a good companion.
Similarly, Juliet's two references to birds give us insight into her nature: they are references to tamed or controlled wild things. She wants a falconer's voice to call Romeo back and she wishes her were a bird on a string that she could pull back at will.
As for the nightengale and the lark, they tell us both about Romeo's nature and also about the nature of the relationship between the two. Romeo, the romantic, is willing to let reality be named or interpreted any way Juliet wants, provided he can have his Love. This moment sparks a kind of crisis for Juliet, for she wants to control him, but she also wants him to stay safe. Just as she has with her references to the wanton's bird (she says she fears she might kill it with too much caring), she realizes that she has the potential to kill Romeo with too much control. When she finally acknowledges that it is day, she acknowledges that though she desires control, she does not want it at any cost, and the life of her loved one is more important to her than the control he gives her.
The references to the bird imagery allow us insight into the character