I proffer 2 composers whose music spans the gigantism of late Romanticism through the period of flux that was C20 in Wester Art music. In fact both of them were major influencers of the subsequent styles.
(In)famous for his 12-tone serial technique, Schönberg's early works are paeans to the aesthetics of German Romanticism: dense, lush, complex, emotive, emotional & all of the other clichés of Romanticism. Illustrative works: Verklärte Nacht & Gurre-Lieder.
Before WWI Schönberg sought a way to progress his musical style & experimented with explicit atonality. Although works like the 5 Orchestral Pieces, Op 16, don't diverge radically from the late romantic style (one could argue that the lushly orchestrated work is a highly compressed Gurre-Lieder with added dissonance), works like Pierrot Lunaire begin to create a new textural as well as harmonic vocabulary.
Post WWI we see Schönberg's "method of composing with twelve tones which are related only one with another" come to fruition. Exemplary work is this style are the Suite, Op 25, & Variations for Orchestra, Op 31. Interestingly, for all of the novelty of the compositional method & harmonic language, these two works are both exemplars of backward-looking forms: the Suite evoking (more or less) the forms of the Baroque keyboard suite; the Variations a massive set of orchestral variations on a original theme in the Romantic style; both relying heavily on contrapuntal techniques to provide an aural compass. It's perhaps the small-scale music from this period that is most divergent stylistically: e.g. the Op 33 Piano Pieces.
Brahms was still writing when Stravinsky was born & the Beatles had broken up by the time Stravinsky died! Few would disagree that Igor Stravinsky was a giant of European Art Music through C20. Early works were in a Romantic style showing the influence of his teacher, Rimsky-Korsakov, & other Romantic influences. e.g. The Firebird
After WWI Stravinsky's style evolved into a less indulgent (in terms of forces & gesture), post-Romantic neoclassicism. Illustrative examples from this period in his writing are Apollon musagète & Symphony of Psalms. While neoclassicism isn't a musical period per se, it is an aesthetic movement that was very influential on inter-war Western Art music.