Which battle was more significant the Battle of Trenton or the Battle of Saratoga?

Its difficult to say, because both were crucial. Without Trenton the Revolution would probably have collapsed at the end of 1776, so the state of affairs where Saratoga took place ten months later would never have been reached. And without Saratoga the French most likely would not have interceded on behalf of the Americans, and without French help the Revolution would not have ended successfully. As events played out both were necessary for an American victory. It is a matter of opinion then which was most important, or indeed if either can be said to be more important.