They are similar in that they both care for the young lovers. They both want to see them happy. They both hate the feud that is going on and have hopes that it will end.
The differences are that Friar Lawrence has served the Montegues for a long time, but he is not as close to Romeo as Juliet's nurse is to her. The Friar is willing to help Romeo and Juliet be together and the nurse is not.