Since this is, imo, one of the clearest dichotomies, I'd like to actually do a reality check on it.
From experience, it manifests in self-reports as such: Intuitive types will describe themselves as being "top-down" thinkers. In Rick's words, "more aware of the overall system and less of the details". Sensing types OTOH probably will not have a good formulation of the way they think, but be more aware of the results of it--true to being more aware of the details, and less aware of the overall system. I've yet to hear a Socionics-ignorant Sensor make any comment on the way they think, at any rate.
Beyond that, I'd say that Sensors (based purely on the way I think) are "ground up". Working with details first causes the overall system to slowly come into focus. Logically, Intuitives would work by being aware of the details they lack and working toward them (though I've only heard this attitude explicity from LIIs, so it may not be a "general Intuitive thing").
My reality check is thus: do the Sensors here relate with this description? The Intuitors? Completely, or in a slightly modified sense? How?