We'll have to agree to disagree. I think the visualization you linked to is much harder to read, because the visual weight accorded to each edge is a non-linear (and somewhat arbitrary) function of the 'true' weight. It also doesn't scale well with number of vertices.

Whereas with the chord diagram, your eye is naturally drawn to the big arrows, and you can easily follow them. It's also bidirectional in a more straightforward way.