Is there any reference for comparing publishers (or at least major ones)? Writers choose a publisher based on fame or by chance, but is there any system for rank of publishers? Or providing statistical data such as the number of published volumes, magazines, factors of business success, etc.
Well I don't really think there is a clear answer in this case. You might be able to pull the information together by looking through Locus or other field related magazines. Even so with a bit of looking around I can find some older rankings of publishers. Such as the 2011 Ranking of the Global [Book] Publishing Industry and the 2011 Publisher Survey Results. That might provide some of the information you are looknig for.
That being said, most writers will choose a publisher based on what they publish. You wouldn't send a piece of military sci-fi to Harlequin, they would never be interested in it. On the other hand Tor on Baen books might be a much better fit. You want to find a publisher that is already in that field. This is true for both books and for short fiction.
Keep in mind that a most of the book publishers want submissions to come in through agents, on the other hand a good agent will know who the best publisher for a story is. As for finding an agent, it will work much the same, find one that works in the field your trying to write for.