One similarity between the declaration of independence and the bill of rights is that both documents

Both of the rights had similarity which is to empower the people to have more freedom, freedom to act and to speak their mind freely. 

In the documents, the declaration of rights eventually declared what was suppose to be done and while the bill of rights had protected the rights of the people and to stress the liberty. If you can research on it, you can understand that the government has limitations in terms of power.