In my experience, minidisc has one very serious advantage over
MP3 players: cheap, interchangeable, small media. In something the size of a packet of
cards, I can fit five
hours of
audio for a cost of about US$8 (that's about four minidiscs, folks). I can change from one to the other in 2 seconds; and I don't need to be near a computer to do it. Another serious advantage of
minidisc is the ease of editing track information: labelling tracks, inserting new index points, reordering tracks,
deleting and
inserting tracks at any point in the minidisc without losing time, and so on.
Another disadvantage of cassette tapes is the sounds quality decays over time and cassette players need to have their heads cleaned and/or demagnetised in order to sound good. With all the other media, provided you are careful, the quality remains the same.
One further disadvantage of cassette tapes and DCC's is that they are sequential access media; which means if you don't like a song, you have to fiddle with fast-forward and reverse to find the next song, whereas with the remaining media are random access -- you can jump to any point in the recording.