By the Estates General, I assume you speak of the Third Estate which later comprised the National Assembly. I'm not sure one can distinguish between the two. They definitely wanted equality--to be treated more fairly--but this could not be done without limiting both the power of the king and the privileges of the First and Second Estates. All three estates agreed on the need for a Constitutional Monarchy and the need to protect individual rights. Still, the Third Estate was often outvoted by the other two, who did not wish to surrender their privileges. The National Assembly actually approved a Constitutional Monarchy in which it held all lawmaking authority.