Like you, I also enjoy both classical music and dubstep as my two favorite music genres. I also began taking piano lessens just over 4 years ago and now enjoy playing works by many of my favorite classical/romantic period composers (such as Beethoven/Chopin/Liszt/Schubert/Grieg etc.), and I can't help but notice these same types of similarities.
@Doc as well
I think I can also add more citations. On the classical music side, I've really enjoyed works such as the Prokofiev Piano Concerto #3, and Beethoven's Piano Concerto #4.
For some cool Dubstep peaces, I would point you toward Daybreak by Overwerk, Illusion by Obsidia, Warrior Concerto (aptly named) by Glitch Mob, The Alchemist's Nightmare by Varien (which has almost some operatic component), Mirrors also from Varien, Timestretch by Bassnectar, Better than Expected by Insan3Lik3, and many others I'm sure.
A lot of these pieces have such a wealth of different sounds, and quite a range of contrast too. I almost picture it as a type of symphony or concerto; each sound placed as a different voice of the orchestra, a different instrument perhaps alternating between the melody and accompaniment.
Now I'm not comparing all of these recent (last few years) songs to Beethoven or Prokofiev... But I think I can see parallels, literal and stylistic, in terms of certain elements of composition. I also think this is only the beginning... New electronic artists seem to be popping out faster than ever with the wide availability of the software (and they often give away there songs for free) - who knows what the increasingly popular genre might evolve into.