I've been riding for 29 years now. My last bike was a 2004 Kawasaki Concours and while it had its detractors, it was a good machine and a lot of fun.
I replaced the Kawasaki with a 2006 K1200LT and I'll never look back.
With the Concours you could drag the pegs through the twisties, it would launch like a rocket and getting to the plugs was a piece of cake. After adding a 45 liter Givi box, it had tons of storage space - even more than the LT.
That's where the good ended though. The Concours had that ever-present vibration that put my right hand to sleep after 15 minutes of riding. You won't have that with the LT and if by chance you do, a quick flick of your left thumb will set the cruise control and you can stretch to your heart's content.
Then there's the brakes... If you have to make a quick stop on the Concours, ya better be prepared for a rear wheel lock up 'cuz it's coming!
On the Beemer though, brake as hard as you want - though with power assist it doesn't take any effort - and you'll stop as straight as an arrow. On top of that, there's virtually no nose dive at all. Even being 200 pounds heavier, I'm sure the LT stops quicker.
Top heavy? They both feel top heavy at slow speeds, but once you get either of them rolling, it's all good. The LT would not be my first choice for an everyday city of Boston cruiser, but then neither would the Concours. I'd prefer a '78 Yamaha Daytona Special, but that's a whole 'nuther story.
While the Concours will carve up the road, the LT will surprise the heck out of you. As big as it is, it sure doesn't feel like it until you start dragging pegs. At highway speeds and above (80+) the Concours was very susceptible to any sort of wind be it a headwind a crosswind or a draft from passing a car or truck. It was about as aerodynamic as a dumpster. It was like riding a sail.
The LT on the other hand was surely designed in a wind tunnel. Even cruising at triple digits, you feel secure and you aren't constantly ducking in as low as you can behind the windscreen to reduce your shape.
For 2 up riding there's no comparison at all; plain and simple, the LT owns the road. Your passenger will thank you for it.
If you think you need to keep the Connie for one-up riding go ahead and do it, but I think you'll sell it next year when you realize the 4 carbs are getting gummed up again because you aren't riding it enough.