I go by artist (performer) and then by work. But having just changed from an old ipod to an android phone with extra memory card, I'm still unsure how to work things out best.
And I have no symphonic stuff on there so far, just concertos, chamber and solo piano music ... guess I'd go with composers in case of symphonies, but that would still look weird, having Mozart or Mahler in the artist listing next to Rubinstein and Rabin.
It would be nice if these new devices would indeed depict all those fields you can enter tags into, and let you sort by whatever you want (my android phone doesn't even recognize all the genres, some R&B works, some is displayed as Soul/R&B, some is - with some of the classical - in a separate category called "ta", whatever that stands for.
Silly new world.