The main advantage is that a differentially hardened katana can take and hold a sharper edge for longer.
Using the Rockwell Hardness Scale, most well made Monotempered katana have a HRC in the low 50s. When differentially hardened, the spine stays at around HRC 40 and he edge hardens to 60.
This extra hardness means it can be sharpened more than a softer edge and will hold the sharpness for longer without needing to touch it up. The softer spine also allows some extra shock absorption, though ONLY if you cut with perfect edge alignment.
The other reasons are mostly the traditional aesthetic of a real hamon, but yes, it does have some pratical differences and advantages, it is not just for show.. (unlike folding, which IS just for show these days thanks to the quality of modern steel making it an obsolete practice, and one which does more harm than good on any blade less than the $500 price point or thereabouts).
Hope this helps.
Much Thanks by: Anonymous
Thanks that clears up the confusion. Awesome website by the way. :-)