Of course, these documents do not completely contradict one another. The Constitution sets out ways to protect the people's "life, liberty, and pursuit of happiness." However, the spirit of the Constitution and that of the Declaration are certainly different.
The Declaration emphasizes equality and popular control of the government. It says that all men are created equal and that the government only governs with their consent. By contrast, the Constitution is less concerned with equality and more concerned with insulating the government from the people. The Constitution sets up a system in which the House of Representatives is directly elected by the people but the Senate, the Supreme Court, and the President are not.
The Constitution is more of an elitist document created to take power (to some extent) away from the people. This contradicts to some extent the idea of equality and popular control of the government that is in the Declaration of Independence.