The conflict between Creon and Antigone is one of conflicting values and duties. Creon is trying to establish himself as king. In Creon's mind, since Antigone's brother Polynices violated the laws of the government, he does not deserve a respectful burial. Antigone has a different perspective formed from her beliefs in the gods, burial and familial love.
Both Creon and Antigone act in the way they are convicted is right. Creon, in his pride, goes so far to establish himself and honor the laws of the city that he neglects some of the gods' burial laws. He is strict in his retribution of anyone who disobeys because he does not want his new power tested and found weak.
Antigone believes she should answer to the higher beings of the gods when it comes to a question of burial, even under the threat of death. She also recognizes that had she lost a husband, or a child, she could have or find another, but with her parents dead, she cannot find a new brother. She has lost both of her brothers in one day. She is grieving.
Both Creon and Antigone are characters who stand by what they believe in, even if it makes them opponents. Creon protects the laws of the city and his throne, while Antigone honors the gods and her family.