Epitaph is something written or said in memory of a dead person; especially, words written on a gravestone:
Alexander the Great : “A tomb now suffices him for whom the world was not enough”
Winston Churchill: I am ready to meet my Maker.
Whether my Maker is prepared for the great ordeal of meeting me is another matter.
Epithet, on the other hand, is a term used to characterize, or to describe, a person or thing. For example, famous leaders are often identified with an epithet, as is the case with people like Alexander the Great, Richard the Lionhearted
Epithet can also be in sense of an offensive word or name that is used as a way of abusing or insulting someone or others: “Friends generally hurl one epithet after another at each other when they get together after a long time.”
An epitaph is sometimes a statement that tells monumental lies or epithets above about the person who lies below.