24 bit offers more detail than 16 bit, so in a comparison between a 16 bit source and a similar 24 bit source, the 24 bit recording will always win based on sound quality. Compare the original Nintendo Entertainment System that was 8 bit with the new systems like the XBOX 360, Wii, or Playstation 3 that are 256 bit (I think). The new systems' graphics look more realistic because they can display more detail.

Basically, the sound waveforms we hear live or from vinyl records or analog sourced tapes are round, smooth curves. A digital representation (compact discs, DAT, etc.) of an analog or live waveform looks like staircase steps, at 90 degree angles. In other words, jagged edged instead of smooth and rounded. As you increase the bit depth, the steps become smaller and higher in number, so they more closely resemble the ideal round, smooth analog waveforms.

You can read more here:

http://www.24bitfaq.org

http://24bit.turtleside.com