It seems to me that in a paper of this magnitude, the only way to approach it would be to divide and conquer. If you keep trying to compare and contrast two different characters throughout the paper you will not only confuse yourself but confuse your reader. You could devote the first eight pages exclusively to Hamlet and the next eight pages exclusively to Antigone. Then you could use the remaining pages to compare and contrast the two characters. You would be in a much better position to compare and contrast the two characters after you had seen what you yourself had written about them. In other words, your documented research could focus on them separately, and your conclusion could be entiely your own opinions. I believe that Plutarch did something similar to this in his classic Lives of the Noble Greeks and Romans.
I think that one of your challenges right now is that you might need to find some aspect or basis upon which to launch your comparison of both protagonists. I hear you correctly when you are seeking to write a comparison paper between the both of them. I guess my follow up question to this is what are you going to compare in both of them? Are you going to compare their efforts to go against the status quo in the pursuit of their vision of justice? Perhaps, you are going to compare how each of them seeks to establish justice when it goes against the law? Maybe another form of comparison is how they treat others around them in a manner that belies the nobility of their quests. I think when you are able to determine what aspect you are going to place focus on in your comparison, you might be able to see the writing process advance a bit farther than where you are now.
Hamlet is a Revenge Tragedy. You could do a comparison contrast type paper, comparing Hamlet to one of the following plays, which are also considered Revenge Tragedies and were written and staged during the same time as Hamlet: The Spanish Tragedy by Thomas Kyd, The Revenger's Tragedy by Cyril Tourneur, or The Maid's Tragedy by Francis Beaumont and John FLetcher. The first instances of revenge tragedy plays were staged in ancient Greece and Rome. You could also use one of those to compare to Hamlet; Seneca's Thyestes is considered possibly the most influencial ancient revenge tragedy upon the English Renaissance.