I wonder if more than one or two folks have owned both.
I had the pleasure of an extended drive on a 2015 K1300S Motorsport Edition before settling on a 2007 K12. Full disclosure, I have owned a LT for the last 4 years and have taken it on several extended and cross country trips)
I wanted to expand my riding options, and so, through a friend, angled the ride on the K1300s.
Now I have owner the K12S for about 2 months and I am settling into it. I am not a particularly aggressive operator.
From my perspective, the K1300 offers quick shift (up shits only) - pretty cool and definitely cuts down your quarter mile time. K12S doesn't
K1300s has more refined fairings. I like the rough edginess of the K12
K1300S has about 8 more HP. FWIW, not material unless you are jonesing to loose you license faster than with the K12S
Oh, and the K13S Motorsport Edition has the very expensive adjustable foot pegs. For me, no added value other than they look cool.
And it has the forged wheels, which I believe reduce the unsprung weight by about 2 lbs per wheel. If you are really into competition, this could be material. Not so much for everyday.
Thats my $ .02
Really enjoying my K1200S !!!