Similarities
Both want to see a union between the two.
Both Friar and Nurse work together (in a way).
Both are not nobility yet have ties to respective noble families.
Differences
Nurse (her past) primarily tied to Juliet while Friar's was to Romeo.
The inept plan was largely the brainchild of Friar not nurse.
Nurse is more forward than Friar. She openly defends Juliet in front of Capulet. She initially has more to lose. Friar does stuff in secret.
They could have thought about the myriad of things that could go wrong with the Friar's rather inept plan. Both were adult figures yet they satisfied the passions of two impulsive teenagers. They might have proceeded more cautiously.