Compare and contrast Yeats's "Leda and the Swan" and "The Wild Swans at Coole."

Apart from their both dealing with swans, in my view these two poems on first reading have little in common. "Leda and the Swan" is a sonnet based on the incident in Greek mythology in which Zeus takes the form of a swan and seduces (as some accounts put it) or rapes a woman, Leda, who is the wife of Tyndareus, the king of Sparta. "The Wild Swans at Coole" is the reflection of a young person about his own life and his process of maturing, of essentially losing his innocence, while the "nine and fifty" swans he observes at Coole are a constant, unchanging element of nature, never aging. The speaker then speculates that some day, the swans may in fact leave the lake and go elsewhere "to delight men's eyes."
If there is connection of thought or theme between the two poems, apart from the presence of that particular bird in each, I would suggest that it lies in the preternatural quality Yeats attributes to the swan in both. In "Leda and the Swan," the bird is a god in disguise and therefore immortal, mysterious, and all-powerful. It almost carelessly forces itself upon the hapless mortal Leda, and at the end its "indifferent beak" lets her "drop." Yeats alludes to the Trojan War and its aftermath, given that Leda is to become the mother of both Helen of Troy and Clytemnestra (wife of Agamemnon). Thus the rape of Leda is viewed in the context of a collective human tragedy that will result at least in part from this initial act of violent cruelty.
In the other poem, the unchanging and seemingly omnipotent swans are similarly contrasted with the speaker and his own sadness: his "heart is now sore" as he thinks of these brilliant creatures, indifferent to him and the comfort he used to gain from them (which is gone now that he's older). He asks "among what rushes" they will "delight [other] men's eyes" when they have abandoned him, having flown away to give the comfort he has enjoyed to others.
"The Wild Swans at Coole" is the more "conventional" of these two poems, with its oft-repeated trope of a poet addressing and bonding, in some way, with a bird figure that represents or reflects elements of the speaker's mind, his joy and suffering. In "Leda," the swan is a remote figure attacking a human being and a seeming cause of generalized suffering as well. But in both cases, the bird is intimately connected with human experience, for good or ill, mystical and somehow delineating the ups and downs of men and women in its mutely disinterested way.