Obviously, the story of La Llorona (a mainly Mexican-American/Southwestern tale) and the Greek myth of Jason and Medea are very similar. For those unfamiliar with the latter: Medea was a barbarian princess who fell for the Grecian hero Jason. They married and had two sons, but years later he left her for Creusa, the princess of Corinth. In a rage, she murdered their two children and sent a poisoned dress and crown to Creusa, who died in agony immediately after donning the fatal garments.
One of the most interesting parallels is this: in both versions, the woman is seen as less "civilized"- La Llorona is a poor girl from the rough, earthy society of the New World, Medea is the daughter of a barbarian king- and the man is the cultured one- Jason is a member of the highly refined society of classical Greece, the conquistador who betrays La Llorona is from the "refined" European world. One wonders whether this is xenophobia ("Those damn uncivilized foreigners- they'd even kill their own children!") or sexism ("Women... they're so unreasonable and hard to control!"), but in truth, it's probably a combination of the two.
One thing that is different in each tale is where the sympathies of those who hear the tale are meant to lie. La Llorona is an object of fear- this is a tale that has been used to keep children from playing near rivers after dark, which is certainly a valid way to try and stop a dangerous practice- but she is also an object of sympathy: what she did was horrible, but she was driven mad by her lover's desertion, and she is now paying a horrible price for her sin. The blame in this story is mainly cast on the conquistador- if he hadn't betrayed the mother of his children- and indeed, if he hadn't seduced a young woman out of wedlock- none of this horror would have occured. In the classical myth, however, it is Medea who is blamed. In the story of her love for Jason, she was previously portrayed as a good woman who engaged in wicked actions. After the murder of her children, she becomes utterly evil- she later appears in the myth of Theseus as that hero's murderous stepmother. Jason is not censured for treating her cruelly- or if he is, as occurs in some classical versions of the tale, after Medea's killings he is absolved of any guilt. But it is he who suffers for the deed- Medea escapes from this, as from all later misdeeds, unscathed, leaving Jason to bear the agony of having lost his sons and future bride. And in La Llorona, it is the woman who suffers. In each version, the one seen as less guilty is the one who endures the greater consequences. Is this why they are seen as less guilty, because they are absolving their culpability through suffering? Or is this simply one of those cruelly true mythological commentaries, that great grief can strike people who don't deserve it? (Though of course, in these cases, as judged by modern sensibilities, they really do.)
Whatever the intricacies, the theme of this story is one that strikes a deep chord- and because it does so, it has surfaced in these two distant cultures, years and miles apart, to assert itself in the conciousness of those who hear it.