Oh yes we do. Music today is orders of magnitude more in all directions that you want to explore "music space". Mozart would feel he is in paradise if he were resurrected today, sooo much to explore, sooo many more options. From instruments to the variants of music, not all based on the European system, to how easy it is to listen to music at any time, anywhere (even if the quality is not concert hall, even a mediocre player beats not having the option at all).
I play (alto and soprano) recorder and violin, amateur-casual, and listen to almost all styles there are at least occasionally, and depending on mood and context find amazing things in many places. The kind of music Mozart knew is such a small subset.
What may have suffered, not sure, is the ability to play an instrument. Given how easy it is to listen to music made by others anywhere there is no need to learn how to play. On the other hand, using computers and modern music tech in general you can compose and play music that Mozart had to get a hundred people together for, and you don't need to train your synthesizer to play your notes.
When I imagine I would meet a medieval society the one thing that I would want to bring is a synthesizer (and solar panels and good speakers), and a huge electronic library of music. We have come a looong way in the last one- to two hundred years, with ever increasing speed in new musical developments.