It may be regional, but they do eat both. Just according to my mom's philosophy, a hen used to make medicinal soups are more healing... yeah... I don't believe it... but it's just culture. I say silkie tastes just like any old other chicken..but I've only eaten it as part of soup containing things that make the house stink and smell like feet... yeah.... it's like one of those things like eating hen ovaries to increase fertility...
Eastern medicine does have it's merits, but just like western medicine that can over do things... so can eastern medicine.
The concentration of the pigment proteins are so little, I don't know if they really do that much for you or affect the flavor as it's in the connective tissues.
There was some study saying that the levels of pigment are elevated (duh), but that they haven't found any thing "special" about it.