Communist, I'm not entirely sure if Alistair's remark is based on your question, I may well be to "Put"'s.
The question "who is the best composer in the world" is by definition an unanswerable one, for reason that one cannot possibly know all music by all composers (even when one narrows “of the world” to “of Western music”) and even then one cannot apply strict “scientific” measurements of greatness. Because of that alone the question of “who is the greatest” is a silly one indeed!
If you would ask me “who of all composers and their music you know has made the most deep, profound and lasting impression on you”, I would answer “J.S. Bach”, for he manages to do with some simply looking music (a few notes, a few lines) things another composer might need a whole symphony.. But I do not compare him to other composers, because such is impossible. How can I compare Bruckner’s symphonies (who I love deeply) to Bach when Bach composed no symphonies? Or Monteverdi’s operas to Bach when the latter did not compose operas? Can you compare Vierne’s organ works to Bach’s? No, you cannot, for the reason Bach’s music isn’t Vierne’s, and Vierne’s isn’t Bach’s. The closest I can get is my personal opinion that in the music of Bach all development of that era found its zenith, and that much of what came after would not have been what it became if it hadn’t been for Bach. Of course, all composers stand in the development of music, like all things alive stand in the evolutionary development of life on this planet. But to me, none has been such a crux in that development. Had Bach not existed, Bruckner might have written his symphonies, but I believe they would not have been (i.e. been less) what they are if Bach hadn’t been somewhere in Bruckner’s musical genes.
I am very much aware of the fact that the above may be put rather clumsily, but it may give you an idea of the shape of the reason why I think the question of “who is the greatest composer” is, indeed, a silly one.
All best,
gep