If so how do they compare to each other?
Not sure if this is AskHistorians matter, but in case it is: yes. In Islamic eschatology, the dajjal (Anti-Christ?) will proclaim himself to be the Messiah. Then Isa (Jesus) will descend from heaven, battle it out, and ultimately kill the Anti-Christ, before establishing a period of unprecedented peace and prosperity.
(note: in Islamic theology, Jesus is still alive)
However, being mortal, Jesus will eventually die, and that would herald the start of the destruction of the universe. After that will be the Qiyamah, or Judgement Day.
This doesn't seem to be a historical question as much as a theological question.