This is a great question. There are many differences. So, I will only mention a few.
First, it is important to ground these two plays in history. Euripides in writing for the Athenians in the 400s BC and Seneca is writing in Latin for the Romans during the first century AD under Nero. Some 500 years separates the two works.
Second, if we start with Euripides' work, Medea comes off as a tragic figure. She is strong, but she is also a victim. We are able to sympathize with her plight and there is a sense of pathos. We might even be tempted to say that she is an unfortunate victim of the gods or fate. When we look at Seneca's play, we feel little of these things. Medea right from the beginning is a frightful figure. She immediately is filled with rage and plots her revenge. The start of the play says it all. In Euripides account, Medea speaks of her suffering; in Seneca's she prays for revenge.
Second, the relationship between Medea and the gods also differs. In Seneca's account, the gods are challenged and even cursed; in Euripides' account, Medea capitulates.
We can look at Seneca's version as a retelling, since Euripides' Medea was well-known in the ancient world.