Oldish thread, and I guess you've probably got it all figured out by now, but here's my 2 cents. I own an '08 K1200S and I love it. But I have test ridden the K1300S, and I was VERY impressed. Very slight changes in the angles of the bars make her more comfortable in the wrists and arms, the engine feels much smoother (though I didn't feel any noticeable difference in power) and the quick shifter is just brilliant. All said and done, the differences weren't enough to make me switch, but I still remember that test ride fondly every time I see a K13S. Both are brilliant bikes, but the K13S shows a level of refinement the K12S can only envy.
2006 IBlue BMW Z4 MC
(OZ spec) - ESS VT1 Supercharger, KKS gated exhaust, TMS camber kit, ST Trophy BBK with CL R6E pads, Ultimate pedals, PerformanceBox, Street Wheels/Tyres: Volk G2s and Potenza, Track Wheels/Tyres: Volk TE37SLs and BFG R1 slicks, Recaro Pole Position (driver), APR GT wing, OEM front brace, Carbon engine cover