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 VT2-525 Supercharged, JRZ RS1 suspension (500#F, 600#R) with Vorshlag plates, ST Trophy BBK with CL R6E pads, KKS gated exhaust, TMS sway bars, RE rear camber arms, VT engine mounts, Recaro Pole Position (driver), APR GT wing, Street: Volk G2s and Potenza, Track: Volk TE37SLs and BFG R1s.