If you own a PC and need to carry large amounts of music around, then an MP3 player is probably the way to go. MP3 has no copy protection, so you'll be able to trade without loss in sound quality.

However, if the type of music you regularly listen to requires higher fidelity, then go with a MiniDisc player -- its advantages are only distinguishable if you know what nuances you're listening for in your music. You'll have a format that's close to sounding like a CD, only lighter and more convenient.

One distinct advantage of MiniDisc is that ATRAC is specifically designed to record music. Another advantage of MiniDisc is being able to record live audio using a microphone.