Joint stereo is a method to save some bandwidth by encoding certain parts of the spectrum in mono (i.e. only once) for which the human ear has no directional hearing. These are very low and very high tones.
The bandwidth is saved by recording a wider sum channel and a narrower difference channel, where the difference channel does not contain these spectral components.
This works very well and produces excellent quality at 128 Kbit/s for most pieces of music. The Fraunhofer codecs, for example, use this method.
However, there is one drawback. Some music contains sounds that are deliberately delayed or phase shifted. Such effect boxes are called "flanger", "phaser" and the like. If you encode such music in joint stereo, you will have bad cancelling effects where the high tones appear and disappear all the time, destroying the good original sound. One old example is the accompanying guitar in Paul Simon's "Mrs. Robinson".
Other encoders, like Lame or BladeEnc, record both stereo channels entirely separately. They are free of these distortions. However, to reach the same overall quality, they need some more bits, i.e. at least 160 Kbit/s.
Thus you could try Fraunhofer at 128 Kbit/s first, then listen for any distortions and, if you hear any, abandon the compressed music and compress again with Lame or BladeEnc at 160 Kbit/s or more. But, as memory becomes ever cheaper, you might as well use Lame or any other good encoder with separate stereo and variable bit rate encoding from the start.
Another way out of the dilemma is to use MPEG-4 AAC, which simply has a better compression algorithm and reliably produces excellent quality at 128 Kbit/s or even at 96.
To state that "joint stereo" is better than "Stereo" is false, it's not. Many times it may save space by making certain parts "mono" (i.e. changing it and assume you cannot hear the difference) but to say that it is better is ignorant.