In April i travelled 560 miles on my 2007 R1200RT ( A truly brilliant motorcycle ) to view and buy a 2004 K1200GT with 8000 miles on the clock.
My initial feelings on taking it for a test ride was that there was something seriously wrong with it, particularly at low speeds where i felt that it just wanted to fall over in a turn. I have over 40 years of motorcycling experience, much of that as an Advanced Police motorcyclist and this bike felt dreadful.
Checking the obvious first i found the front tyre ( Michelin Pilot Road ) was well down on pressure and correcting that and increasing the preload on the rear shock made a BIG difference but this bike will never handle as well as a 1200RT. That said i have now done 3000 miles on it and as a long distance mile muncher it is very good and fast sweeping bends suit it well.
I think the biggest problem you have is that you are comparing the K1200 against an R1200 and they are as different as chalk and cheese.
One is very light and one is very heavy.
The K1200 has 20 bhp more but on the road i think the R1200 is probably a faster A to B bike due to handling.
Which bike is better to ride either slowly or quickly? NO DOUBT ABOUT IT R1200RT.
Which bike looks best NO DOUBT ABOUT IT K1200 RS/GT.
I have settled into the K1200 and the handling is no longer an issue.