Ah... Let me share the results of my research.
I had experience with Bilstein's before and was very happy with them. Apparently many others shared my experience. On the other hand, I also hear many good things about Koni. Trying to figure out which one was better just gave me unnecessary headache. I did extensive research and found that neither is better than the other. They're just different.
- Koni Sport is rebound adjustable. Bilstein isn't. That's not a huge issue if you don't need adjustability. You can argue that adjustability can actually work against you if you don't know what you're doing.
- Bilstein seems to last longer than Koni's in term of maintaining the damping characteristics, but you can use the adjustability on the Koni to compensate for that. They are both significantly more durable than the stock units so this isn't something I'd worry about too much.
- Now the most important difference, Koni Sport will work better with softer spring rates while Bilstein's work better with higher spring rates. To over-generalize, Bilstein's will handle better out of the box (in track conditions). Koni Sports can be stiffen up to match the Bilstein's or even out-perform it by a tiny margin (as tested by Car & Driver), but at those settings it's not any more comfortable than the Bilstein's.
Ok, now you just have to find out whether your springs have relatively low or high spring rates and whether you care about comfort more or at the limit handling.
p.s. auto-x folks (myself included) will tell you to get Koni's. Reason being, auto-crossing is very different from tracking. A stiffer suspension works better on the track while auto-x favors a more compliant setup.