...ew
Anyway. Most well-known modern composers aren't trying to write things "similar" to Bach or Brahms, etc. because we don't live in the 1800s. There's a bunch of very well-known composers from the early-mid 20th century including Bartók, Schoenberg, Stravinsky, Shostakovich, Prokofiev, Webern, etc., but there's also a bunch of fairly-well known composers that are either still alive or died fairly recently (from the 80s on).
I'd recommend getting away from the idea of "this is what I want music to sound like"; it closes you off to a whole world of interesting things.
Some widely recognized pieces by the aformentioned early 20th century composers are things like:
Schoenberg - Moses und Aron (opera)
Bartók - Concerto for Orchestra (it's a pretty easy piece to "understand"; there are also things like the string quartets which are just as important but less friendly)
Stravinsky - Symphony of Psalms
Shostakovich - String Quartet No. 8; Symphonies Nos. 5 and 10
Webern - Bagatelles for String Quartet; Piano Variations. (pretty much all of Webern's mature work is difficult to approach, give it time)