I can't give an opinion on a K1200, however I have "just" bought a K1300.
I was coming from a 2002 R1150RT (Which I still have and is for Sale if anyone wants it)
, and decided I wanted a newer bike. I considered a newer RT, but then I saw the GT; a (little) less tourer-like, with a slightly more sport riding position, and higher rev range.
I saw and agreed to buy a 2008 K1200GT, but then saw a 2010 K1300GT EE. I actually bought the bike based on photos and videos, and had it couriered to me from Ireland to the UK.
All I can say is I am glad I did! The K1300GT is an awesome machine. I have thus far only completed 2 rides, as I only got the bike yesterday. The first ride was 6 miles to work, straight out the back of the couriers van, and the next was about 15 miles home from work. Hopefully I'll get out on it over the easter weekend.
However, thus far I am totally besotted. The bike plods along at 30mph happily, granted only in 2nd gear. Open the throttle and your clocking 100 before you know it. On my bike at least, the gear changes apart from into 1st are smooth and effortless. I suppose at twice the horsepower of my RT and less weight, it should be quicker, but I would venture to say the K1300GT is the perfect bike. I can't wait to see how it handles the twisties of Wales over the next few weeks. It certainly doesn't feel heavy when its moving.
The advice to me was buy the newest one you can afford, so I went with the K1300GT, and have NO regrets, after I scraped the bottom of the piggie bank.
If you haven't made the decision already....get the K1300GT!