I've seen a lot of bad press about the K1600 which is a shame as it could be a cracking bike. A recent MSL article didn't put it in good light either saying go for the R1200RT not just because of teh K1600 issues but its a better all round bike - seems a no brainer
Having owned both I'm in a good position to comment.
The engine is smoother and has no noticeable vibration on the 1600 and is a leap ahead of the RT.
The gearbox on the 1600 is better but the RT has the smoother drivetrain and doesn't have the same level of backlash as the 1600.
Brakes. Little in it on both bikes and I wouldn't say one is better than the other. Both have excellent brakes.
Screen. Standard screen on the 1600 is better (for me) than the RT,
Fairing. RT fairing gives better protection out of the box than the 1600.
Comfort. The 1600 has more room for rider and passenger than the RT. SWMBO rates the 1600 as the most comfortable bike she has ridden pillion on and better than the RT. Not much in it from the riders perspective, though the 1600 does have slightly more leg room than the RT.
Running costs. The RT is easier on fuel but not by as much as you would think. My RT averaged 53mpg over the time I had it and the 1600 has averaged 50.5mpg. The 1600 is harder on its tyres, with fronts lasting 6000 (7500 RT) and rears in the region of 5000 (7000 for the RT). Brake pad wear seems to be about the same for both.
Servicing would favour the 1600 for the 6 & 12k services, but the 18k is the biggie for the 1600, but I haven't had the 12 or 18K yet so I can't give specific figures.
It's not as much as a no brainer as you would think Andy. Both are very good motorcycles with pros and cons.