Generally it is the force that is important - not the energy but.
There's a simple misunderstanding here, in that looking at E = 1/2 mv2
Let's carefully look at the units - mass * velocity * velocity
Now velocity is distance / time
So we end up with (mass * distance2)/time2
So we can see that by halving the time it takes to deliver a technique - we get 4 times the energy.
Now lets look at F = MA
That is mass * acceleration >> acceleration being distance / time2
So (mass * distance)/time2
Meaning once again if we half the time taken to deliver the technique we get 4 times the force.
The main difference between the two is that for Energy we want as much mass as possible travelling as fast as possible, for Force we want as much mass as possible travelling as fast as possible to stop as quickly as possible.
If we look at modern cars - they travel the same speed as old cars - but have crumple zones at the front so that when they hit something they slow down more gently. The energy involved is the same - but the force is lower because the acceleration is more spread out - making it more survivable. So in general it is the force that matters. Humans can travel very quickly indeed (kinetic energy) its the sudden stop that kills you (force).
Now when it comes to knocking someone out - there are so many more variables than energy and/or force - (such as the location and direction that that force/energy is applied). The main thing to realise is that the defender wants to minimise the force and energy that they receive - either by dodging the attacks entirely - or reducing the speed with which a technique hits (thus reducing energy equation directly and the acceleration/deceleration part of F=MA) - or lengthening the time over which the technique hits (again similar effect to both equations - a lesser deceleration).