It's usually the sound effects that are screwed up as I think they just record the music into a file instead of generating it.
Exactly, you are correct. However on the SEGA Collection, the sound is actually emulated, they even credit Steve Snake for the YM2612 core in the credits!
But I can forgive Capcom Classics Collection though, because Quiz and Dragons is in my top 10 games of EVER list.
Actually the music on the Sega Genesis collection is Streamed off of the disc. The way I know this is that the music was skipping until I resurfaced the disc even though there were no visible scratches to begin with (Weird). Ever notice when you play Phantasy Star 4 the music doesn't stop right when a battle ends? Also, laser beams don't make the Beeewwww sound. Other than that game, the overall emulation is pretty good.
One thing that makes me mad is how DE did the worst job ever on TMNT Arcade for X-box 360. No video (other than resize), sound or game options and you only get 1 life so when you die like every 15 seconds on some of the bosses the music starts over after the continue screen.