Dido, in Virgil's Aeneid, is one of the many abandoned woman in the literatures of the world. How would you compare her reaction to her abandonment to that of Medea in Euripides's Medea?
As thanatassa explained, there are some definite similarities between Medea and Dido. Both are women abandoned by the men they helped save, which in turn leads to intense emotional responses. Both of these responses are characterized as madness, and both of them have extreme responses that end in death.
The most significant difference between the two responses is how the women are treated by the stories they appear in. Medea is the titular character of Euripides's play, but that doesn't mean she's the hero; despite her being our focal character, her actions are pretty despicable. She poisons Jason and her innocent children and flies away on a chariot drawn by dragons sent by her divine grandfather, Helios. Her connection with magic and sorcery runs deep, especially as she's often characterized as a priestess of Hecate, the Greek goddess of magic, necromancy, ghosts, and poisonous plants, among other more benign things. Because of these connections, Medea is more closely associated with evil; her actions are violent and brutal against others rather than herself. Importantly, they're also choices she makes. Her acts of vengeance are things she chooses to do, even if they are inspired by the wrongdoings of others.
Dido, on the other hand, is a more tragic figure. The story doesn't absolve her—in fact, when Aeneas and Dido meet in Hades, she turns away from him—but it does paint her as a more sympathetic figure than Medea. In the Aeneid, Dido and Aeneas fall in love through the machinations of Venus and Juno; while they might have found each others' company enjoyable, the gods exert direct influence over their interactions. Mercury is also to blame for Aeneas needing to leave Carthage, taking much of the agency out of Dido's hands. Her actions are not necessarily noble or entirely her own—the manipulation of the gods means that even she is confused by her own actions, lamenting, "What madness/ takes me out of myself?" The result is that, despite her cursing Aeneas and indirectly alluding to the coming Punic Wars, Dido feels tragic rather than villainous. Her poor decisions are inspired by the way the gods use her rather than being entirely her own; while Medea chooses to kill Jason and her children because of his abandonment, Dido is manipulated into falling in love, and her lover is taken away from her, making her madness more god-ordained than Medea's.
Essentially, Medea is angry, and her choices lead her to commit vengeance. Dido, comparatively, is confused and hurt, and her actions lead her to kill herself and curse Aeneas. Neither is particularly noble, but the source of their emotions—Jason's taking of a new wife despite his promise, versus the gods' manipulations—change the way we view each character's actions as an audience.
Both Medea in Euripides’s play Medea and Dido in Virgil’s Aeneid are women abandoned by heroes. In both cases, the women helped the heroes and were repaid by being abandoned. Medea killed her brothers and permanently alienated her family to help and follow Jason. Dido risked her position in her kingdom to help Aeneas.
Both women, it could be argued, went insane. In Dido’s case, she became distraught, cursed Aeneas, and killed herself. In Medea’s case, the anger turned exclusively on Jason and she killed Jason’s new fiancée and her own children to harm Jason. In Dido’s cade, grief accompanied and overwhelmed anger; in Medea’s case, anger overwhelmed all other emotions.