Jim,
I am a Koni fan. Unfortunately, I can't compare Konis to Bilsteins, but I can say that I am completely satisfied with the Konis.
The only Konis available for 113s are the Classic line. They are not gas pressurized (makes installation easy), and they have three adjustments for the rebound (extension) damping rate. The compression stroke damping is fixed.
I installed them at setting 1 (softest) as recommended, and the ride is great. In this setting, I would characterize the ride as very, very slightly underdamped. Very smooth and comfortable, yet still well controlled. I've not tried the stiffer settings, I see no need to.
Biggest disadvantage to the Konis is the 113 shocks are not stocked in the US and have to be special ordered. Took about 2 months to come in. I ordered them through Tirerack, about $90 each.
I also installed Konis in another car, and they transformed the ride from "buying this car was a mistake" to acceptable. Magic.
George Davis
'69 280 SL Euro manual