I own a minidisc deck and portable, and I recently got an MP3 CD player (the portable kind). I have to say, for convenience, the MP3 CD Player rules. You can fit hundreds of songs on one CD and you can burn as many CDs as you want, and they are dirt-cheap. You can even use CD-RWs if you want to rerecord over old stuff. You can burn a CD in less than 20 minutes, while to make enough minidiscs to hold 200 songs would take a looooong time. And although they have some good points, I don't think the solid-state MP3 players compare because the media is SO expensive.
I loved my minidiscs for a while there, and MD still has some advantages right now, such as much better anti-shock, battery life, price, etc., but I think that those things will improve in the MP3 CD players. I would say Minidiscs are still better than MP3 players, but MP3 CD players are the best IMO.