The difference in the continental 'slicks' is that you are relying on a different weight source for the momentum of the cut. With an English-style slick, you have a massive tool whose own mass is enough to keep it going. With the continental variety you are positioning your body above the cut and relying on your own mass, which is significantly greater than the tools, to make the cut.
The big difference I see is that the tools are adapted to different ways of working. German and French carpenters worked with their timbers on or very close to the ground, and so they can very easily put their own mass behind a cut. English and American carpenters liked to put their timbers up much higher, where it is impractical to try and put your weight behind a cut, and so instead they make very large tools with a great deal of mass of their own.
If you are going to be working with timbers at or above waste height, then you had better use a slick, if you will be working with timbers lower than this than you should use you body weight to your advantage as much as possibly, in which case the continental varieties may prove more effective.
It should also be noted that the English were typically working with much bigger things than the Germans were, for example joint sizes. German mortises are a lot smaller, and a smaller tool is needed. English mortises are huge, so a huge tool is nice.
If you are going to be doing things the way most American TF'ers do it, then you should use the familiar style of slick -it is adapted to this way of working. If you however opt to work with low timbers, the Stichaxt is a great way to go
DLB
