The K1300S is an incredibly awesome, very refined bike. But the S1K is the best in the world for the intended goal; speed, power and agility.
For the time period that I owned each, my riding patterns were/are the same. I rode the same number of miles, about 1,500 miles per month.
The K1300S takes less discipline to stay comfortable. The S1K is a track day bike. The key to comfort on the S1K is to be disciplined enough to ride in the position for which it is designed. If a rider stays tucked and keeps the elbows bent, then the bike is very comfortable. I am 6'2"' 250#, when riding the S1K as it is designed, I found the bike to be very easy to ride for longer trips.
That is not to say that a rider can be a slouch on the KS. But the KS is the best in the world for its designed goal, it is a sport touring machine. It is an awesome 2-up, sport-touring bike.
The huge factor for me, I learned to trust both bikes. Each bike is reliable, very well engineered and, the electronics are a modern marvel. Trust is something that I did not have so much with the Hayabusa.
The two BMW bikes are aimed at different market segments. But again, both are the best.
One more note, the bottom end on both bikes (0-60) is equal. Various rags report 2.7 0-60 on the S1K also.