"Style" is complicated to copy in both cases if you don't know what you're looking for.
In music, you have voicing sparsity, changes in voice count, preferred pitch ranges, tension/release cadences, embellishments, richness, playfulness, and a host of other characteristics. Rachmaninoff, for example (among other things), favours active, moving octaves quite deep in the base, extremely rich chords in the middle treble, simple (local) rythymic patterns, and expanding simple ideas like repeated arpeggios into large parts of a piece. He has more voices than other pieces typical of his time, though they tend to be combined somewhat simply when contrasted with counterpoint exercises and other techniques typically involving fewer voices.
In writing, you have sentence length, sentence complexity (they're different), typical volume used to express an idea, specific word choices, whether you tend to observe concrete or abstract ideas, the level of "truth" in your statements (in many flavours -- deadpan humour being quite different from a boldfaced lie directed toward the reader), technique choice used for signposting, willingness to violate "rules," and so on. If you picked even one project proposal from me at $WORK, you could reliably separate it from those written by hundreds of other engineers just by a few quirks -- habitually providing one level of motivation deeper than is typically expressed in technical writing (not just what we're doing, but what we're not doing and why we made that choice), a tendency to use British spellings and US words, a pattern of contracting any verb tense, sometimes with multiple apostrophes (e.g., "there'll've been"), refusing to terminate a non-exhaustive list without informing the reader that it's non-exhaustive, and so on. If you look at the reasons and motivations for one of those quirks, it's that I tend to have complete ideas (in technical domains) and want to express them completely and have found that every missing detail causes eventual problems -- only tempered by the fact that the requisite length tends also to cause important details to be overlooked on a casual read, which provides a mild damper on length. Understanding that motivation makes it easy to apply it as if you were me even when you don't have concrete examples regarding specific quirk/scenario interactions.