I haven't ridden the K1600, but some of my riding buddies have BMWs and I've had a chance to spend time on a K1200GT and a K1300S. Like you would expect and others have mentioned, the big K-bikes offer lots of power, stability, comfort, good handling, and power. At speeds over 40mph, they trounce the Strom in pretty much every way.
But for around town or off-pavement, the Strom is the better bike. And of course there's the huge difference in cost of ownership, which can affect your riding pleasure just as much as handling or power.
2010 Triumph Tiger 1050se
2009 DL650A - sold
2005 DL650 - dearly departed
"I am enthusiastic over humanity's extraordinary and sometimes very timely ingenuities. If you are in a shipwreck and all the boats are gone, a piano top buoyant enough to keep you afloat that comes along makes a fortuitous life preserver. But this is not to say that the best way to design a life preserver is in the form of a piano top. I think we are clinging to a great many piano tops in accepting yesterday's fortuitous contrivings as constituting the only means for solving a given problem." - R. Buckminster Fuller