There was a tremendous amount of work done that morning to keep the site up. Basically the site went static for long periods, which was the only way to save the poor database servers that were screaming and bleeding from their eyes under the load. If I recall correctly there was an after-action report posted later about the technical aspects of keeping the site working that day. Slashdot had nothing near the infrastructure that many "medium-sized" websites have today, which was bad: didn't have enough hardware to survive, but also good: the bosses were close enough to the metal to make immediate programming changes to reduce the site loading.

So it's really the opposite: Slashdot was unprepared for bursting of this magnitude, but able to react reasonably quickly to combat the unpreparedness. Other sites were probably more prepared (CNN.com) but once the load exceeded their preparations, it took them a while to, you know, get permission from the big boss to make the site static and otherwise react. CNN and other major sites did get their act together in fairly short order, actually - it's not at all the case that they were down for an extended period - they figured things out pretty quickly, just not quite as quickly as Slashdot.