These two documents are similar to one another mainly in the fact that both of them are concerned (at least in part) with creating a limited government.
One of the major ideas of the founding fathers was that the U.S. government should not have unlimited powers. Americans had felt that the British government had too much power and they did not want another such government. Therefore, they set up a constitution that would limit the powers of the government. Within the Constitution, for example, the government is forbidden to pass bills of attainder or to suspend the writ of habeas corpus. Similarly, the Bill of Rights lists many things that the government may not do to infringe upon the freedoms of the people.