Edit: More information. It seems that the WL algorithm leads to wider less distinct channels, causing high topographic index values (my final derivative data set). The image on the left below is the PD algorithm, the image on the right is the WL algorithm.
These images show the difference in topographic index at the same locations - wider wetter areas (more channel) in the WL pic on the right; narrower channels (less wet area) in the PD pic on the left.
So the differences, however small, do seem to trickle through the additional analyses.