As one of the many who has complained about the adjustment sensitivity of the SA 8-speed hub, I think I should mention that several months ago I put a Nexus red band 8-speed hub on my old Trek touring bike and set it up so the gear range would match that on my Downtube Mini as well as possible.

In favor of neither hub, I must mention that the two shift in opposite directions; on the Shimano, turning the shifter towards the thumb is an upshift, on the SA the same motion is a downshift. This is annoying, and makes it difficult to switch back and forth between bikes with the two different hubs; I will probably solve this problem by mounting the Nexus shifter on the left handlebar. Oh, and just to keep everyone on their toes, the Rohloff shifts like the Sturmey Archer, and the NuVinci shifts like the Shimano.

Otherwise, the steps between the gears of the Nexus seem much less even than those between the SA; as a result it seems easier to find the right gear on the SA than the Shimano.

Both hubs may unexpectedly slip into a lower gear if something goes wrong with the shift-- if you inadvertently turn the shifter, for example, or if you inadvertently prevent it from turning a the whole gear increment. The same thing can happen if you have the cable adjusted wrong.

This leaves two questions in my mind:
--is the Sturmey Archer mechanism more difficult to adjust than the Shimano's? Not to me! but perhaps this is a matter of familiarity (I am more familiar with the Sturmey Archer).
--is the Sturmey Archer mechanism's adjustment more sensitive than the Shimano's? I suspect it is, but I am not quite sure yet. The difference is subtle.

All in all, at this point I cannot say either the Shimano or the Sturmey Archer 8-speed hub is vastly superior to the other. In general I prefer the shifting of the Rohloff and NuVinci, but the latter have their own shortcomings --price and weight, respectively.