The score was effectively re-composed for the later film, with Bernstein taking its basic components and redeploying them in often entirely new musical and filmic contexts, while also combining them with his own newly composed music and further preexisting material from Herrmann’s rejected score for Hitchcock’s Torn curtain (1966).
Bernstein later said that Scorsese “wanted the atmosphere that [Herrmann’s 1962 score] provides” and that it was “much more appropriate for the remake…the first film was not up to the strength of that score.”
This according to “Cape Fear: Remaking a film score” by Jonathan Godsall (The soundtrack IV/2  pp. 117–135). Below, Cady’s ill-advised release from prison.