I sell both... Won't surprise anyone when I say Koni over Bilstein for the exact reason MFE mentioned--adjustability.
You can do an awful lot to how car responds, turn-ins, take a sets, and even the confidence in you have it when you can play with damping. This isn't a dream, it's why so many high end cars now have adjustable dampers on them, cars like ZR1's, Porsche Sport Packages, Ferrari's.... Those companies understand that there isn't one setting that will suit all persons, all the time, in every situation.
Bilstein's are great dampers in terms of quality and ride, but when dealing with increasing springs rates, less travel, and a performance need like HPDE's then I think you want something that gives you options and doens't just make you settle for "good enough".
7x SCCA National Champion + 7x SCCA ProSolo Class Champion, 2009 SCCA ProSolo Overall Champion
I drive them, I compete in them, I sell more variety of brands than any other company.