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.
One thing you can do with the Nexus 8spd hub is to get a Shimano trigger shifter made specifically for the hub.. inadvertent shifts vanish and more positive shifting ensue... I use one on my Swift.. big difference.. well documented on MTB forums also..