But musicologists look at pieces differently. They see it perhaps from a historical perspective. As I mentioned with the Beethoven, they notice that he is stressing third relations in the 4th piano concerto. G major phrase answered with B major (a third above). Second movement in E minor, a third below. Last movement, which has to be in G major according to Classical style, starts in C major, which is a third below E minor. Musicologists and theorists know this is interesting because the Classical period stressed, not third relations, but fifth relations: G to D, not G to B. Fifth relations are clearer and stronger. But Beethoven was more and more experimenting with the basic principles of Classical style. Incidentally, Charles Rosen has written a couple of books that are extremely intelligent discussions of just what Classical style was all about. I distinguished musicologists and theorists but officially all study of music except performance and composition is called 'musicology'. However in practice theorists tend to be the folks that analyze pieces in great detail, while musicologists look at them in an historical or social context. There is a lot of overlap, of course.
Composers look at things still differently. It is not just the case that they are always looking for something they can steal (after filing off the serial numbers), but there is some truth in that. Other composers are looking at the kinds of challenges the composer took on and how he solved them. As Bernstein once is reported to have said: "Bach, that pregnant syllable that causes performers to weep, composers to fall to their knees and that bores everyone else to tears." Bach, and Beethoven too, are the ones that composers (up until the rise of modernism) would be most amazed by because of the incredible focus and dynamicism of their music. Write an entire volume of fugues on a single theme (with variations)? You're kidding! And exhaust every contrapuntal possibility? Or write an entire symphony largely based on a four-note motif consisting of only two different notes? This is the kind of thing that most composers know is simply beyond them. Which is often why they end up throwing everything but the kitchen sink into the piece with predictable results.
Modernism made a serious break in this historical relationship. Beethoven in his Diabelli variations could look across the wide gulf in time to Bach's Goldberg variations and know that they were the main players in the big league. Even as late as Brahms this same sense of historical connection was there. But with the serialists, the futurists and even the neo-classicists (who mimicked the outward appearance only) there is little sense of this great tradition.
But let's listen to a couple of those pieces, that stick out of the stream of music history like great peaks or crags. Both pieces are in several clips on YouTube and I have only put up the first parts so you will have to search out the following ones. First Bach, the Goldberg Variations recorded by Glenn Gould in 1982:
Then Alfred Brendel playing Beethoven's Diabelli Variations: