I am not too sure about your hints you have been given, but I will compare the two characters in this amazing short story. Remember that we never actually meet Michael Furey, but his surname, resembling Fury, seems to signify a lot about what his character represents. He, although he died young, was able to love passionately and intensely, in a way that Gabriel never did. Thus his name seems to suggest fury against the paralysis and stagnation that other characters, such as Gabriel, evince in their willingness to accept the status quo and never truly experience love and life. We are told that Michael Furey dies for Gretta and that he did not "want to live" because he knew he was losing her.
This causes Gabriel to reflect on his own superficial and meaningless existence, and how he has never truly loved and cannot share in or understand the love Gretta had for Michael Furey. Consider his following thoughts:
Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age... He had never felt like that himself towards any woman but he knew that such a feeling must be love.
Hearing of his wife´s relationship with Michael makes him realise that it is better to live life loving rather than "wither" up without experiencing those emotions, and Gabriel cries at this knowledge and loss. The evocation of Michael makes him see himself for who he truly is: "a ludicrous figure... a well-meaning sentimentalist... the pitiable fatuous fellow he had caught a glimpse of in the mirror."
Gabriel realises that Michael truly lived, even though he died young, and that he has never lived, and is rather "withering". Gabriel thus sees himself flickering in and out of the shadowy world where the dead exist - there are no boundaries between the dead and the living and thus this explains his reflection that "One by one they were becoming shades."