Highlight at 1:39.
Your highlight doesn't mean shit. As the two halves of the log jump away rather far, he is clearly cleaving the block, not cutting it. A proper cut would result in the blocks falling over at most. Cleaving is something entirely different than cutting. Cleaving just requires force, which means that a heavier blade, which I presume the broadsword to be, would perform better than a lighter blade. Hence why axes have all the weight concentrated behind a rather small blade.
The way he uses the katana reduces the katana to an edge with weight behind it. He is not using the curved blade for a certain cut motion that could perform better than a broadsword, he is just simply chopping. The only variables when testing like this are blade weight and blade sharpness. Which means that a broadsword with the same weight and a similarly sharpened edge would perform the same.
Furthermore this katana or current broadswords have very little to do with their historical counterparts, so a comparison is pretty much useless.
