The 2 bikes are remarkably close- although I see the GT actually has a taller saddle height! Wheelbase & O.A. length very similar/same (respectively), but the GT comes in at a wet (curb) weight of 590 compared to the K1200 @ 628 (pounds)!
wheelbase: GT 60.5; K12 61
seat height: GT 32.1; K12 31.5
dry weight: GT 558 lbs; K12 586.4 lbs
wet weight: GT 590; K12 628.3
overall length: GT88.6 inches; K12 88.6 inches
HP: GT 128; K12 130.52
torque: GT 108; K12 117
That 40 lb difference in wet weight will make a lot of difference. I'd only looked at the dry weight of the Sprint before, which is very similar to the T160. Other than that, they do seem very similar.
One thing I forgot to mention is that the swingarm was extended for the GT, to keep the front wheel down. Pulling out into a gap in traffic in Yarrawonga on the way to an All British Rally, I found that asn't entirely successful.
We can compare notes when you do manage to snare one.