Further in the case of Mancini v. Goodwin: Mancini wins, with a couple of qualifiers:
The first is probably Hitchcock's own decision, and that's to use NO music at all in the magnificent backwards tracking shot. Just let the deadly silence build the suspense until we get down to the open door and the sounds of the street begin to fade in, proving that no sounds from upstairs would possibly be heard. That scene is pure Hitchcock genius just the way it is.
The other is the sudden flashback moment of Rusk figuring out what happened with the tie pin. What Mancini wrote is fine, but I've always loved Goodwin's brass pyramid over those shots. That entire montage and musical buildup taking us back to the "chase" music is wonderful. It gives the audience just the jolt it needs ... and the volume is suddenly good (see below). Which brings me to:
The recorded sound of the Goodwin. From my very first viewing I was distracted by the generally low volume level of the score (with the exceptions of the main title and the brass moment above), and by the distant recorded sound itself. It's a generality, but the orchestra in typical American soundtracks is "in the room" and an integrated part of the scene, while the orchestra in many European soundtracks -- however perfect the music itself is -- sounds like they're playing in the hall next door, and that we're "hearing a recording" laid on the film. In FRENZY, Goodwin's slow waltz and the more rhythmic suspense themes all sound like they were recorded in the middle of an empty ballroom. But then think of PSYCHO, and how that string orchestra is right there, practically on the screen and driving the scene. And even that one brass moment I love in FRENZY that's at the proper volume nevertheless has an artificial-sounding acoustic that I just don't like.
Anyhoo, the Mancini score is classic and classy, and I think the movie would have been better served by it.