MiniDisc is a digital medium, not analogue. Therefore, any differences in sound quality are simply a function of encoding/compression (if used at all) bitrate and the quality of the playback equipment (speakers, leads, amp, etc.)
This is, of course, assuming that the master copy that is used is the same in all cases. An external source of perceived quality differences could come from different mastering used on different releases of the same music. A good example is the so-called "loudness war" (Google it for more info) where older releases of many music tracks sound a lot better than later releases even on the exact same medium and encoding.
The CD standard uses uncompressed audio, while MiniDisc uses a proprietary compression system which is also "lossy", meaning that it discards some of the theoretically inaudible sounds in the original uncompressed copy. MiniDisc audio does not require decompression on playback, as the compression is accomplished by discarding "unnecessary" data.
MiniDiscs therefore have, unquestionably, worse audio quality than CDs.
If you take the exact same recording and put it on a CD an a MiniDisc and play both through the same amp and speakers, the CD will sound better.
It's a different matter when it comes to other digitally compressed music, like MP3 and similar formats. With these it depends on bitrate and specific codec.