Up until this trip, I hadn't ever been to any kind of ballet or opera, but I've had the opportunity to do so as part of this trip.
On 7/3 I saw a ballet at the Alexandrinsky Theater, a "modern" ballet based on Chekhov's The Seagull, which I haven't read, and so my understanding was fairly limited, though I got the gist. There was one part where everyone was break dancing to a hip-hop beat--that was fairly entertaining to watch, as it seemed fairly incongruous. For the most part I enjoyed it, but certainly I can live without it.
On 7/16 I saw La Traviata at the Mariinsky. The theater was certainly amazing, and I enjoyed the show, but to the same extent that I did the ballet. It was nice, but I can live without it. It was an amusing situation, that the performers are of course singing in one language I don't understand (Italian) while it is translated into another language I marginally understand (Russian). But I got the gist: Love and Death. Of course, that's simply the basis of pretty much any such drama.
It's hard to say which I liked more; both the ballet and the opera have a different appeal. The ballet is much simpler and concentrated on gracefulness, whereas the opera is a fairly rich, majestic production. I guess it's somewhat similar to the difference between a silent film and one with sound, in that you need to squeeze every bit of symbolism and artistry out of the former, since you don't have the "crutch" of dialog.