FWIW, I just did the transition from a '99 Connie to an '03 K1200RS (it and the GT are very close cousins). In general, the K1200's strike me as German Connies that moved up-market. All the things I liked in the Connie (day-long quick riding with reasonable comfort) are there. The K1200's don't feel as "tippy" as the Connie although I suspect the RT's COG is lower (maybe not?). The really good news is the Beemer motor pulls like a freight train and the brakes do their job without a lot of fuss and with ABS. In fact, when I went looking for the replacement to Barney, ABS was a must-have.
The down side is the complexity of the Beemer. Changing the air filter means pulling the gas tank (honest!). It's a lot harder to add electrical farkles (horns, lights, etc.). Even a lot of the fasteners are not the usual metric bolts and screws but either Torx or hex screws/bolts (the problem here is more adding new tools to the tool box - as fasteners go, I like Torx fasteners over standard bolts).
Misc. pros and cons... the K's handling is (surprise!) really confidence-inspiring. The lights... it's too easy to outrun them at night - plan on changing to brighter bulbs or HID's. The centerstand on the K actually works without threatening to blow your back out or give you a hernia. The Connie bags hold more than the Beemer bags. The Beermer bag mounts are more robust than Connie antlers and you don't need to unbolt antlers and cover the bolt holes up with tupperware, as on the Connie, if you want to ride without them. The seat is as comfortable (or not) as the stock Connie seat. The Connie seat is vastly easier to take off and put back on. The K's seat, in its lower position, will have you sliding forward and jamming "the boys" into the back of the tank - bet on it. In the upper position... not so much. I may look for a Corbin replacement, as I did on my Connie.
I put something like 40K on the Connie before the engine hydro-locked. I had a lot of fun with the bike and was truly sorry to see things end, at 61K on the clock and a lot of riding otherwise left in the bike. In the roughly one month I've had the Red Flash so far, I've done two 300+ mile trips and some local riding. Would I buy the bike again? In a New York minute!
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ADD: I installed an after-market AudioVox cruise control on the Connie. My KRS has the OEM cruise control. The AudioVox unit worked well, although I quickly learned to keep my weight off the throttle grip (and on the handlebar end weight) while it was engaged. The BMW unit doesn't much care about that, but if you hit a bump on the road and accidentally back the throttle off, the cruise control disengages (as it's designed to do). In general, with a real cruise control (as opposed to a throttle lock - IMNSHO, a near-suicide device), long distance slabbing becomes much, much easier. Don't leave home without it.