The international landsknecht community & home of Stockholmsfänikan
This is a great picture! Never seen it before.
One thing I've learned over doing reenactment is that there is nothing that a Bidenhander can do that a halberd (or even, at times, a pike) can not do or improve upon. It is perhaps for this reason that the time period where the Bidenhander was used is really small and these weapons ended up unused in armories and museums. The stuff that worked was used and seldom survived.
In the Battle of Kappel, two handed war swords are depicted; however, they are simply large, two-handed swords without the parrying hooks / lugs above the ricasso. But, judging by their clothes, these soldiers are most likely not Landsknechte.
Even in a picture depicting soldiers that appear to be in Landsknecht styled garments, their swords are still basically a standard cruciform two-handed sword (albeit a big one).
From what I have gathered (although I do not have any sources to quote or cite), the more fancy swords (flambert blade and lugs) were predominantly used outside the fields of war. When maintaining peace in a town or in the encampment, they are intimidating and demonstrate stature and rank. From what it looks like, the image that Berthold posted depicts something in a castle or in a town, not the standard pike square the Landskenchte are known for.
But we come back to the fact that a halberd does everything a Bidenhander can, a halberd is cheaper, a halberd has a greater range, and it is little surprise we see more Landsknecht with a halberd on the battlefield.
Taking a look again at this woodcut, you can see the dopplesoldner has a cruciform hilt sword with a leather ricasso. This is a 1530's woodcut I have seen many times, it is a little hard to notice, but on the blade forward of the ricasso are two bumps, maybe the style developed from this into the parrying hooks? Take a look: