There are two main ways in which Euripides make Medea more sympathetic to the audience than Seneca.
First, Euripides makes Medea into a victim, who acts out of her pain. She is the one who is forlorn and devastated by the actions of her husband Jason. Euripides also has a third person speak of Medea's plight and pain (the nurse). In this way, the audience is called to share the sympathy of the nurse.
Sencea's version of Medea is much more active. She has been wronged and she will now wrong Jason. She is a frightful person of exacting vengeance. Since she is portrayed in this active way, there is little sympathy that the audience can give. She is more than capable.
Second, Euripides makes much of the gods. What happens to Medea has been the horrible lot of the gods. She has been cursed. In this way, Medea is put into the category of a innocent victim. She even asks the gods for mercy. Seneca's Medea uses the gods for vengeance. She even says, "Vengeance, O God, come to me now!" This is very different than Euripides' Medea who says, "Would that I could die!"
In conclusion, the passive nature of Medea in Euripides evokes sympathy, whereas the active nature of Medea in Seneca evokes fright.