I only hope that Mr. Williams doesn't follow this discussion board. I agree with several of the preceding posters. His film music is very good but I wouldn't say great in an abstract, apart-from-the-movie sense. He has catchy, sometimes memorable themes/melodies and excellent harmonies and orchestration but something more deeply profound is missing. I like his scores for "Schindler's List", "The Book Thief" and "Empire of the Sun" best. I find the "Stars Wars" scores to be among my least favorite, primarily because they beat those main themes to death, and they are kind of hoky.
To my mind, he shares one thing together with Leonard Bernstein (as a composer): I sometimes have the nagging sensation that the melody or certain harmonic figures have been "borrowed" from previous composers. I am not talking about plagiarism, but rather too close an absorption, imitation of, or influence from some earlier composer. This is not a sin: there is no great composer who did not learn from or borrow from his/her predecessors. But sometimes with Williams and Bernstein, the influence just seems a little too direct. This seems particularly true for me with Williams' score for "Saving Private Ryan". Kind of Coplandesque.
I think the comparison of Mr. Williams and Korngold is apt: both wish to/wanted to be both semi-popular film composers and "serious" composers. Perhaps you can't have your cake and eat it too.
Don't get me wrong: I admire Mr. Williams' musicianship a great deal. I myself would not be able to score a 30 second toothpaste commercial successfully.
As a film composer, I like Alexandre Desplat a good deal. But I find that as he writes more and more film scores, the musicianship and quality seems to be decreasing. His earlier scores are best, to my mind. But he is not in the same classical orchestral tradition as Williams. It's a little more intimate, like chamber music.