Eumaeus and Melanthius are like polar opposites.  Eumaeus is a shepherd and Melanthius is a goatherd, which to me, immediately says something about the two characters.  It is weirdly symbolic relating to religion.  A shepherd is always seen as a good thing, the Bible often talks about shepherds and Jesus himself is the metaphorical shepherd of all the people.  Shepherds are also often referred to/thought about as good leaders, faithful to their flock, responsible, and kind and gentle.  On the contrary, even the word goatherd has a different feel and stigma to it.  Who wants to be a goatherd?  Who's even heard of a goatherd?  Just with this information we begin to think of Melanthius in an unsavory way, and we find out that his character reflects it.  Eumaeus proves himself to be a "good shepherd."  He stays faithful to Odysseus while he is gone, and when he sees the poor "beggar" (Odysseus in disguise), he welcomes him.  He gives him food and shelter when he needs it, and it shows the Eumaeus is a generally nice man who looks to do what is right.  Melanthius on the other hand supports the suitors, betraying King Odysseus.  He looks out for only himself, and shows an evil side more than once.  He is selfish and cocky.  He wants Telemachus dead, and when the beggar comes to the palace, he treats him with disrespect and cruelty.  These two characters are an interesting comparison in the story.