Beethoven's music is unmatched in terms of sheer emotional power, while Mozart's music in unmatched in terms of perfection, simplicity, and beauty. To state that one composer is "the greatest" is very tough, as music is fleating: it depends on your mood at any given moment, and taste fluctuates with time.
For example, Beethoven's 5th is universally acknowledged as a landmark in western music, yet it isn't always appropriate. I personally wouldn't put myself to sleep on it! By the same token, Mozart's 21st Piano Concerto is a marvel, but lacks certain components that Beethoven's 5th symphony possesses. This piece, on the other hand, is good sleeping music. Therefore my personal taste depends on my personal condition at any given time.
With all of this said, if I had to create a list of my favorite composers, I would most likely say Beethoven, Mozart, Chopin, Puccini, and Grieg.