The Magna Carta established the basis for representative democracy as it was the first attempt after the fall of the classical Graeco-Roman era of a form of parliament, where nobles would meet to deliberate the course of society,and advise the kings on policy issues. It was a paradigm shift from the absolute politics and power structures of dark Europe, forming to inspire future government discussions in England and USA.
The major similarity between these two documents is that both reflect the idea that there should be limitations on the power of the government. This is an important idea that is one of the major bases of our entire system of government today. The major difference between the two is the degree of democracy that they contemplate. The Magna Carta is really meant as a contract between the king and his nobles, giving the nobles guarantees against the king. By contrast, the Declaration of Independence is a call for equality and rights for all people (or at least all white men). This means the Declaration is far more democratic than the Magna Carta.