Michal Furey loved Gretta so much that he, a (probably) tubercular worker in a potentially carcinogenic workplace (the gasworks) risked his already fragile health to come stand in her back garden in a cold rain. He is so desperate to see Gretta before she leaves that he says "...he did not want to live." Gretta believes that he died for her, and it may well be the case. There is no mention of whether or not he wore galoshes, but if he did it didn't save him. He died a week after that last time he saw Gretta.
Gabriel, however, is fond of the newfangled galoshes, and he is careful about his and his wife's health. Unlike Michael Furey, Gabriel seems to relish being alive. He is in love with his wife, but he also does not seem to harbor romantic notions about her. "He did not like to say even to himself that her face was no longer beautiful but he knew that it was no longer the face for which Michael Furey had braved death."
It's hard to imagine Gabriel Conroy braving death for anyone, and certainly not for romantic love. He seems too self-satisfied for that, but he also has, as many smug and contented people have, an element of self-loathing "A shameful consciousness of his own person assailed him. He saw himself as a ludicrous figure, acting as a pennyboy for his aunts, a nervous wellmeaning sentimentalist, orating to vulgarians and idealising his own clownish lusts, the pitiable fatuous fellow he had caught a glimpse of in the mirror."
It is difficult, in this last respect, to compare Michael Furey and Gabriel Conroy. Michael Furey died as a teenager, in all the passion of ill-health coupled with immaturity and intense romanticism. Gabriel is a grown man, a teacher, a father and husband, with all the cares, maturity, satisfactions, and even dashed illusions that that status conveys. Michael, the passionate lover of Gretta who sang, with a beautiful voice, the maudlin tune of "The Lass of Aughrim" had none of Gabriel's life of solid -- and, perhaps, stolid -- respectability and responsibility. Such circumstances change personalities.
But, it is suggested by Joyce's text, Michael and Gabriel shared little except their love for Gretta. Michael is headlong, talented, in ill-health, but also careless of life. Gabriel is, by comparison, careful, steady, respectable, and bent on the enjoyment of his possessions (especially Gretta) and his raised status compared to many people around him. They seem to be of very different dipositions, and, at the end of the story, Gabriel and the reader are left to think whether Gretta would have been happier with Michael Furey, had he lived.
The first big difference, of course, is that Gabriel is alive at the end of the story and Michael has been dead for some time.
The enotes study guide on Joyce's short story points to other meaningful items of comparison and contrast between the characters, including:the significance of their names and their different temperaments. Here's a quick, representative quotation: "Michael is an example of living life passionately, where Gabriel Conroy lives it more timidly and passively."