Fruity, my (probably flawed) understanding:
Resistance to bump motion is mostly a function of the bump valving, i.e. how restrictive the valve is. All else being equal, a twin tube damper with 'stiffer' bump valving will tend to have less bump motion than a mono tube with softer bump valving, and vice versa. So, I doubt that any difference in bump motion between the B6 and the Koni dampers will be due to one being mono tube and the other being twin tube (or in the difference in gas pressure, though this won't have zero effect), but directly due to any 'stiffness' difference in the bump valving.
However, mono tube dampers do generally have larger diameter pistons than twin tube dampers. Larger pistons means larger piston seals with a greater contact area with the damper tube wall. Greater seal / tube contact area creates greater friction and 'stiction' than with smaller diameter seals with less contact area. 'Stiction' means a resistance to initial movement, i.e. the stationary seals 'stick' to the tube wall which requires a certain amount of force to 'break them free' and get them moving. So, mono tube dampers tend to require a bit more force to start the piston moving, but once the piston is moving the 'stiction' disappears. I suspect that this may be where the idea of mono tube dampers having a 'more immediate' damping effect may come from, i.e. the greater 'stiction' effect gives the impression of 'more immediate'. And, somewhat harsher, which is arguably true.
There is still friction created by the piston seals, and larger seals mean (all else being equal) more internal friction as the piston is moving. Once the piston is moving this friction has some degree of damping effect, added to the hydraulic damping effect. The hydraulic damping effect is far greater than the damping effect caused by the seal friction, but can be significantly more when the seals are new (i.e. before 'bedding in'). This is why dampers can feel a bit stiffer when brand new and often seem to soften just a bit after some use.
Due to greater 'stiction', mono tube dampers can tend to feel a bit harsher than twin tube dampers on smaller bumps and rough surfaces (not so much more substantial bumps as 'lumpy' surfaces, with numerous smaller 'bumps'). With a bit less seal 'stiction' twin tube dampers tend to be a bit smoother riding on roughish surfaces and smaller bumps, but this doesn't necessarily mean less damping effect on larger bumps and undulations. The larger piston in a mono tube could be seen as disadvantageous due to the tendency to greater 'stiction', but mono tube dampers have other advantages, especially for a damper in extremis (i.e. being worked hard).
Larger pistons will mean more fluid moves through the valves as the suspension moves. So a larger diameter mono tube damper piston implies that for X damping effect a mono tube damper will have freer flowing valves than a twin tube damper with a smaller diameter piston (through which less fluid passes). This may be one of the advantages of a mono tube damper, i.e. for X damping effect more fluid moves through less restrictive valves, which I suspect might reduce fluid cavitation (lessening fluid aeration), maybe...
And, a mono tube damper has the 'working' fluid in direct contact with the outer wall of the damper, as opposed to a twin tube having the 'working' fluid in contact only with the internal tube, and so with an insulating layer of 'non working' fluid between the 'working' fluid and the outer wall. This means that a mono tube damper can get rid of heat more effectively than a twin tube damper (the 'working' damper wall being in direct contact with the surrounding air, as opposed to a twin tube where the 'working' wall is buried well inside the damper). This allows the mono tube damper to work 'harder' than a twin tube, with less heat build up and so a reduced tendency to cavitate the fluid.
Regards,
John