I believe there could is a way to relate, and even compare Hamlet to Everyman. Take, for instance, the fact that Everyman is faced with problems. Hamlet is as well, obviously. Yes, there are major differences between the problems that each of them face, but if we are to compare the works as a whole, than this would be a logical place to start. Then, we could look at each problem that Everyman is faced with, and compare them with Hamlet's.
First, Everyman is faced with Death. It could be compared to Hamlet that he is also faced with Death many times throughout the play. His Uncle killed his father in order to marry his mother. Ophelia kills herself after he has gone insane. Hamlet's mother, Gertrude, is murdered by poison. Hamlet kills his uncle in a fencing match, and eventually, like Everyman, faces Death himself.
Another character from Everyman that could be compared with Hamlet is Fellowship. In Everyman, Fellowship vows to be there with Everyman until he is asked to follow in the journey of Death. Fellowship then declines. In Hamlet, his two best friends could be compared to Fellowship. They are there for him until they are sent in to England with Hamlet after Polonius' death. It is then that they are given the task to kill Hamlet, and they decline. They do not go through with their task.
Kinsmen in Everyman could be compared to Hamlet's mother. She is there for him, loving him and taking care of him. Yet at the same time she is a very confusing character about whether or not she actually believes Hamlet when he tells her that he isn't crazy. So in a way, she is like Kinsmen when she shows the "fake side" of her personality, making it so she is not truly all-together with Hamlet.