An interesting topic... and here is what I wrote:
A significant part of the great appeal of Spider-Man is that he shared with teens from that era (the 1960s) many of the same problems -- insecurity, dating problems, bullying, not-belonging, etc. Peter Parker had a body supercharged with special powers, but his mind was still that of an everyteen underdog who was wracked with misplaced guilt and a devotion to an elderly aunt.
Would the culture of the late 30s have identified and cared about Peter's problemed psyche? Just a guess, but probably not.
The teens of the late 30s had recently emerged from the Great Depression and the storm clouds of world war were amassing on the horizon. They were not so introspective as to be able to easily identify with Peter Parker. Their problems were much more serious than getting marble-mouthed around Betty Brant; they had problems like worrying about how much food was going to be on the table, and were the relatives back in the "old country" okay.
And for every reason why Spider-Man -- a precursor to the "me" generation -- would have failed in 1938, Superman succeeded. They wanted a hero that was a "super" MAN, not a confused boy. Superman didn't have problems of his own, he solved other people's problems. He was the ultimate symbol of hope for better times -- an infallible champion of truth and justice.
It's no coincidence that when Spider-Man gained massive popularity, the times were very different and it coincided with the nadir of Superman's popularity.
These are 2 characters imbued with very different appeals, each custom fit to the era in which they were created.