Every time (of the hundreds) I took the elevator in One or Two I thought "what if", especially after being rocked by the '93 bomb. I never felt that way in the ESB or any of the dozens of other Sky Scrapers I spent time in. The Trade Center always felt plastic.
Because the Empire State Building and the others, were there long before most of us--you never had to fear the established. When the "Twin Towers" were built, they were the new architecture. They were the new "modern" generation. My mother who was born in 1915 (now passed), remarked at the time that they were being built, we should not be building buildings that tall.
Personally, I do not know structurally how the older buildings compared, but the WTC was representative of the 60-70's generation. "Plastic" as you put it. Maybe, we all had a collective premonition, or the terrorists played upon our silent fears. Regardless, they were wonders to be beheld, and deep down they were feared. Ironically, mostly by those who took them down.
Those elevator rides in the twin towers was something else. Always had the fear they would crash. My fear of heights got tested to the max in NYC skyscrapers.