There are three Color Altering Conversion methods:
Color Altering conversion methods are more flexible than Luminosity Based methods. Color altering methods alter the colors in your photograph during the conversion process. This allows you to do things that you can't with the Luminosity Based methods.
First, it allows you to simulate lens filter effects. Black and white film photographers use different colored filters to get different effects. For example, they might use a
#25 deep red filter to darken the sky. Color Altering methods allow you to adjust colors in a similar way. In fact, you can do things with color altering methods that you can't do with traditional filters, like negative colors.
Second, Color Altering methods allow you to simulate film response. For example, you can set the Channel Mixer to simulate the color response of, say, Tri-X or Delta 400 film.
Color Altering methods work great on images that have relatively uniform luminosity but has lots of color differences. For example the building, windows and the sky in this photograph have different colors but similar levels of brightness.
Here's the same image converted using Hue / Saturation Layer Method. There is much more contrast between the building and the sky in this conversion.
Color altering methods takes advantage of the colors in you photograph. If your image has little or no color to begin with, Color Altering methods are no better than Luminosity Based methods.