It's not as simple for me as saying: "Two words: 'precompositional strategy'."
But that's a common thread among music I find interesting. So, the second Viennese school and some later composers who developed more or less systematic theories, like Messiaen, are important. (Yes, I'm omitting some important "neo-serialists" from this group, but it's not an oversight: just a kind of apathy). Even some composers whose strategies are (as far as I can tell!) mostly opaque and inscrutable, like Scriabin, command a good deal of attention.
This includes some writing for keyboards susceptible to a strong formal analysis, such as in Bach, and other composers who inherited or continued to mine the various forms associated with Bach and his predecessors and contemporaries (dance movements, fugues, etc.)
However, I see a kind of formal .... not purity, by any means ... playfulness in, for example, Beethoven's writings, Haydn's, and Debussy's. A sort of playing within the bounds of either established, inherited forms, or within some at times self-imposed constraints, as might be the case in some of Debussy, or Scarlatti, even.
But, there are lots of exceptions: I can't say much about Mozart other than that he knew how to exploit the resources available to him in opera, for the keyboard, etc. Similarly for Schumann and Brahms. It turns out all three of these examples were more than capable of writing contrapuntal music, and did so, but the bulk of their work has something else I can't really describe.
That there is a lot of music that presents primarily mechanical novelties, which occasionally forms an intersection with pleasing music, is also something I accept, and attempt to stay on top of, although I think of this as more of a curiosity or something to play around with during idle moments.
And maybe another category of music could be described as having an intense political and social element which forms its own impulse, and could be analyzed, but which is, to me, extraordinarily effective above all as music in abstractō. I'm thinking mostly of Shostakovich and Prokofiev, to some extent Boulez, by his strong extension of serialism into a would-be cultural program, and many others. Messiaen, although mentioned above, belongs to this group as well. Not that all composers aren't susceptible to this kind of analysis, but the depth of engagement measured in...metronome clicks, or something...seems to warrant its own category.