How do cement boards and Kerdi boards for wall tile compare?
I haven't used KIRDI-BOARD itself, but I have used similar products.  Mostly, the biggest advantages are found in weight and longevity of the material.  The synthetic foam will last longer than traditional concrete and produce significantly less dust when cutting and installing.

The biggest disadvantage will be the cost.  Synthetics (KIRDI-BOARD and similar products) tend to run on the expensive side.  Some quick Google-ing turned up about $10/sheet for 5'x3'x1/2" cement boards.  KIRDI-BOARDs in a similar dimension (4'x5'x1/2") would run about $77.

So ... if you're working on a DIY project, stick with the less expensive, traditional building materials.  If you can afford to buy massive quantities in bulk (or know a contractor willing to do it for you), look into the more advanced stuff.