Mozart vs Beethoven

Beethoven, by far. Mozart was rather cutesy.

Here's the way I break it down, scoring on a 10-point split scale

Symphonies
Beethoven 7
Mozart 3

Very little in the symphonic repertoire approaches the genius, influence, and originality of Beethoven's 3rd, 5th, 6th, 7th, and 9th symphonies, and I wouldn't be surprised if a large poll ranked the 3rd, 5th, and 9th 1-2-3. That said, Mozart's Jupiter Symphony is, IMHO, just as great as those three, and the 39th and 40th aren't far behind, and really all those after 35 (and a handful before them) are still excellent.

Concertos

Mozart: 7
Beethoven: 3

Mozart was the undisputed concerto king. It can be argued that he wasn't best in any other genre, but there's no doubting his eminence here. The Piano Concertos are the single greatest concerto cycle ever, and he pretty much wrote the best concerto for almost every other instrument (clarinet, bassoon, flute, flute & harp, etc.). Beethoven, to his credit, is bested more in quantity than quality. His piano concertos are sublime, especially the last three, and his violin concerto is, I must admit, better than any of Mozart's five for that instrument.

Piano Music

Beethoven: 8
Mozart: 2

Beethoven's piano music may have been even more important, influential, and revolutionary than his symphonic music, and despite the explosion of great piano composers that came after, it can be easily argued that Beethoven still reigns supreme here. His 32 Sonatas are a world unto themselves, and those last 5 especially are cosmic masterpieces that will repay endless listening. Mozart's piano music was mostly written for students rather for himself, but what they lack in complexity and virtuosity they make up for their endless melodic pleasures. I actually feel Mozart's piano music is quite underrated, and taken on its own terms is full of sparkling gems that delight in ways that Beethoven simply couldn't.

Operas

Mozart: 9
Beethoven: 1

Not much competition here. Mozart's Big 4 operas are among the greatest ever composed, really among the greatest works of art ever conceived. Beethoven's Fidelio gets by more on his reputation than its own merits. It's an awkward work that doesn't really gel as a whole. If anything, it feels like one of the few arenas where Beethoven sounded more conservative and regressive rather than daring and progressive.

Chamber Music

Beethoven: 6
Mozart: 4

Extremely close call here. Beethoven's string quartets are justly praised for their formal daring and musical richness. Mozart's string quartets aren't quite as good as a whole, but throw in the Quintets and it's much closer. Beethoven wins slightly on the piano trio and violin sonata front, but Mozart wins in the "other" category that includes great works like his clarinet quintet, oboe quartet, piano quartet, quintet for piano & winds, Divertimento for string trio, Horn quintet, and Clarinet trio.

Vocal Music

Mozart 7
Beethoven 3

The Requiem and Missa Solemnis is close, but Mozart just wrote so much more beyond that including his Great Mass, Ave Verum Corpus, Exultate Jubilate, etc. So again Mozart wins more by quantity than any other criteria.

Total:
Mozart: 32
Beethoven: 28

I guess it could be argued that Beethoven gains a few points by being a bit more original and influential, but even there it's not a blowout. You can't go wrong choosing either, but over the years I've come to appreciate Mozart more and more while I've somewhat tired of Beethoven a bit. Mozart's genius is a bit more subtle, more deeply buried beneath the superficial pleasantries. Beethoven is up-front with his genius in every work, and it can be a bit exhausting by comparison. Beethoven demands much and doesn't have Mozart's capacity to charm, please, entertain, and seduce. Yes, Beethoven rewards the attention he demands, and there's no law that says artists must be coy about their genius, but I think that's why Mozart has just grown on me more over time by comparison because the greatness is more slowly revealed beneath the charm.