Mozart is lovely to hear. I love the Requiem and the 40th symphony, among others. But playing Mozart myself makes my eyes glaze over. I just damned near fall asleep. And some of it is soooo perky. His deepest emotional work, I think, is the Requiem, which may be why it is one of my favorites.
Beethoven, on the other hand, was the original punk rock composer. E.M. Forster recognized the Beethoven effect before Burgess penned A Clockwork Orange. Forster wrote in A Room with a View of Lucy Honeychurch and her visceral response to Beethoven, which always seemed to make her peevish. She elects NOT to play Beethoven when performing for her erstwhile fiance's mother and guests ... and Forster knows why. They're too staid, too confined, to constrained to fully understand what Beethoven means, but Lucy gets it. Her pastor attributes one of her moods to "too much Beethoven."
Anyone who's ever played Beethoven and thought about it can tell you that his music is angry and melancholic, above all. I personally think that every single thing he wrote is a call-and-response argument between him and someone very close to him. Just think of the opening notes of the 9th and then the response notes that follow. Or "Moonlight Sonata"--it's a lengthy argument with a tragic, sad ending. Playing Beethoven gives me the same feeling as listening to Blood on the Tracks. Agitated, nostalgic, sad, argumentative, edgy. It's no wonder Burgess chose "Ludwig van" as the focal ultraviolence trigger.