What exacly is a "greatest composer"? Is it like: the Michael Jackson of classical music? It depends on what one finds the most important quality of a composer, what might mean it could be a composer who's not the best in orchestration, but very creative and has a tons of great ideas put on paper. Or a composer who changed music the most might indicate the "greatestness" of a composer. But that would exclude all new composers, because nothing could be crazy enough the last century. You can't measure how much the composers of the last century might change the music of these days.
So I'll go for Tschaikovsky. My favourite composer is not on the list: Shostakovich. My favourite orchestrator is not on the list either: Ravel.
Well, it's probably a lack in my upbringing, but I'm not a great fan of most music older than, say, 200 years. Not totally true, because I started being interested in classical music because of Mozart. But after listening so much, it has been flogged to death to me, brilliant it may be.