My experience with each is a bit different. I ran Koni adjustables in my last 3 E30 325is cars with Ground Control springs with absurd rates. I also autocrossed a bunch. I eventually put in H&R sports with these shocks but never had it on course as I sold it shortly thereafter.
My current M42 machine has H&R sports and Bilstein sports. Very nice ride, but a bit bouncy. IMO, just a tad under damped on rebound.
To answer the questions (again a good portion of these are with a 325):
1. General ride- Koni= like a track car and a bit much on the street. Billy= more forgiving but a touch bouncy.
2. Compression damping- Koni= Harsh but linear. Billy= perfect.
3. Rebound damping- Koni= perfect on course in the stiff position, a bit harsh on the street on the soft setting. Billy= a bit under damped here.
4. Corner entry- Koni= amazing and perfectly predictable. Billy= a bit slower turn in.
5. Corner exit- Koni= stupid tail happy (325 with MUCH stiffer springs). Billy= a little wiggly but it holds the line and eventually settles down if you don't put in too much input.
6. In corner stability- Koni= perfect when surface is nice but a touch jittery when it gets rough. Billy= a bit better for street use, but again possibly under rebound damped. Again, if you don't get sucked in to giving too many inputs, they are fine.
7. Braking control= no difference to me as this is more spring related in my mind's eye.
8. Acceleration squat- What is that? This is a 318 after all.

Again related to springs and even with the 325, there isn't enough HP to get too riled up.