The purpose of the Olive Branch Petition was to assert the rights that the colonists belived that they had, but also wanted to vmaintain a relationship with King  George and the country of Britain. These people felt that they had to defend their rights against the injustice that they faced, but they still wanted to mainatain a friendship. King George refused to read the petition and felt that it was basically crap. I really do not see any similarites between the Common Sense and the Olive Branch Petition. I do know that King George refused to acknowledge both requests. But the Olive Branch petition wanted to fight for rights, while still maintaining a relationship with Britain. Common Sense wanted to fight for their full independence.