It has to be Vertigo. Not for anything obvious, but more for it's subtleties and it's ability to leap it's emotion off the screen at a level that his other scores come close to, but simply can't compete.
However, either tied with that, or quite possibly upon examination exceeding the obvious Vertigo, is CITIZEN KANE.
I don't think people realize how complex and incredible both the score to that film is, and the film is itself. It is still the undeniable masterpiece of cinema. And a top of all the cinematic wizardry, it has an incredible story that still is effective today.
Now the score is a masterpiece too. First of all on top of writing the tonal range of emotions and catching the action and transitions, Herrmann was also writing in 3 time periods, during which he correctly used non time specific music and time specific music. The best example of how ground breaking his score is, is during a flashback to when Kane meets the blonde in the street in the rain. His cue is suddenly extremely serious, and if you are really engrossed in the film, this shift would be tremendous. Fo r he has setup most of the flashbacks technically (ie: period music). But suddenly here we have this scene in flashback which is completely dramatic. Not to mention that the cue employs a harp ostinato and melodic structure that is the basis of scores like Stargate and Attack Of The Clones. HUGELY INFLUENTIAL cue.
Then there is the truly first use of Cinematic Narrative. Of course, Welles was the first to use the camera as Narrative, but Herrmann and him as team really hit it over the head. At the end, (for those of you who haven't seen it I will not give it away), the camera pushes in to the "focus object", thereby pulling the audience with it (cinematic narrative), but the music ties the narrative all together by illustrating what the audience should be feeling NOT what music goes with picture or the action. It was the first most powerful use of music and camera from the audience perspective. It was as if the audience was on a tour, guided by Orson Welles, and when he showed you what he showed you, Benny handed out tissues. The frailty of life, the meaning of life, dreams, aspirations, love, tenderness, death, birth, sacrifice, greed, honesty, deception, grief, all rolled into one intense moment which is still unparalleled. And then we close with this even more important statement, again via the cinematic narrative provided by Welles and Herrmann, that in society such simple circumstances which are now existing in modern times, is what can create an empire of despair. Money and greed are taking away people's lives and dreams, and cares. And Herrmann only barely touches on a major chord at the very end, which in case you didn't know, was VERY serious for it's time. Studios did not want to leave an audience in a bad mood. His use of the major chord is minimal and detached and only for function.
Evan Evans