Sean- other than the "ole boots" (might fit Woodhall Spa better) comment, I am with you 100%. The suggestion is the WH-O and S-Black are very similar. That was not my experience at all, though I acknowledge that history and association to most anything have a very hard to measure impact on our perceptions.
Beyond the very different visuals, width, and alternative lines of play, I will defer to John's recent experience on how similarly flat both courses are. My seven year-old recollection of WH-O is that it was indeed quite flat. S-Black, though lacking large elevation changes, seemed to be rolling and heaving considerably more, leaving many uneven lies. I found S-Black from two different sets of tees confounding. Didn't have the same impression of WH-O, though I much prefer its club culture.