Myths and epics are similar in that they tend to reflect the values of the culture in which they originated. Epics are especially apt at this, with their central heroes encapsulating traits that are considered heroic to a culture. Think of the difference between the Christian ideals valorized in Paradise Lost and the Anglo-Saxon warrior code valued in Beowulf.
Mythology can perform this function as well, though some argue that mythology is more multi-faceted. Comparative mythologist Joseph Campbell felt that mythology's highest function was to provide a blueprint for individuals seeking to live an authentic life, as in this excerpt from an interview with Bill Moyers:
But what the myth has to provide, I mean, just on this immediate level of life instruction, the pedagogical aspect of myth, it has to give life models. And the models have to be appropriate to the possibilities of the time in which you’re living.
Like an epic, this links a myth to a particular time and place even as it contains a more universal value. Take the story of Persephone and Hades: it does more than offer an explanation for the seasons in that it traces the human journey from innocence to adulthood through the abduction of Persephone, who starts the story as an innocent girl and ends it as a queen who can move between two worlds.
Obvious differences between myth and epics are the lengths of each. Myths tend to be brief, even episodic. The characterizations within them are not elaborate, relying instead on archetypes to make their point. Epics tend to have more fleshed-out characters that the audience follows over an extended period of time. Compare Pierre in Tolstoy's War and Peace with Persephone in her mythical descent to the underworld. Both characters move from innocence to wisdom, but only Pierre emerges as a full character with specific traits and desires over the course of the Napoleonic wars, while the audience never knows much of Persephone beyond what happens to her.