Dear Mitch,
I don't know the difference between K. Kawai and Kawai, if there is any, but the Shigeru Kawais are a truly high end piano. I am a competitive pianist, and in a recent competition in Japan, I was offered the choice of performing on one of four pianos - a Yamaha, a Bosendorfer, a Steinway, and a Shigeru Kawai. Though I went with the Steinway at the end, I was torn between the Steinway and the Shigeru, and found mysely quite surprised at the indecision. My entire life until that choice, I had always found Steinway to be the only choice. (I do suppose every now and then a Bosendorfer or Bechstein will fit a particular piece well, but there's just that great security on a Steinway.)
Anyway, abuot the Shigerus, I have not yet ween one outside of Japan. However, upon Baldwin doing out of business, Earl Wild switched his sponsorship from Baldwin to Kawai, so if he plays a concert near you soon, you can probably bet that it will be on a Shigeru Kawai. (What his personal problem was with Steinway, I do not know, but he has long avoided them.)
Hope that helps answer any questions...
Best,
Bill