This may not matter, depending on how you ride, but there's one thing you should know in comparing these two bikes: the V-strom can't cruise at the kind of speeds a K12GT can handle easily. Sure, you can run all day at 100mph, but the front end gets a bit scary at that speed, especially with luggage. Adding a steering stabilizer will help, but the strom is just not designed for high-speed touring at the level of the K-bike.
For everything else though, you'll be glad you made the switch!
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