Love both immensely...
But unless he runs up against the Bard himself, you know it's almost certain who I'm voting for here. ;)
Wolfgang Amadeus Mozart, baby! :D
@KingCyrus: I had that debate a week or so ago, Mozart vs. Beethoven...and while Ludwig won in the Musicians tourney, I still say that while both are about equal in terms of their genius, Mozart's operas are the tiebreaker, at least for me.
Beethoven? One opera, not too commonly performed today.
Mozart? Many, with multiple hits in German and Italian, with The Magic Flute and The Marriage of Figaro in particular regularly ranking among the world's most performed operas.
(Speaking of most-performed, I just remembered...after Shakespeare, Henrik Ibsen's the most performed playwright in the world today, and he didn't even make the tourney, shame...A Doll's House, Hedda Gabler, The Wild Duck, Ghosts...Ibsen deserved a shot over a couple of the authors who made the cut here...I'm looking at you, Robert Heinlein.)
Anywho, I'd argue that even if you don't like opera, it's the tiebreaker. Both Mozart and Beethoven have piano, violin, and symphonic pieces which are legendary...but Mozart has an undeniable edge in the operatic sphere as well, making him not just more performed and thus arguably allowing him more exposure, but one of the best opera composers of all-time as well.
I'd like to hear your case for Beethoven, though, of you'd like to give it. :)