Hi there!
I took the Repertoire Lists of DipABRSM to make some brief comments over (most of) the 20th pieces and its composers. I know there are a lot of very personal insights, and my written english is poor, but maybe it can help a bit. I've made no comments on technique 'cause the pieces are very dissimilar and because it depends very much on the student and his/her musical skills, especially sight-seeing, harmony and perception. As a general rule, is by far more difficult to read any of these pieces than reading Classical or Romantic repertory of the same level, even more if the student is not acquainted with modern and contemporary music (not only piano, but orchestral and chamber works, opera, etc). Any further information needed, let me know: I'll be very glad to help if possible.
Bartok, Bela (1881-1945, Hungary) - Mikrokosmos 148 - 153 (late 1930's). A fabulous didactical work by the hungarian composer, and maybe one of the most musically accomplished attempts of that kind in any times. It goes from the absolutely begginer to intermediate-advanced pieces such as those. In my humble opinion, what makes it most difficult is the general unawareness of students about 20th century music, 'cause I can't figure another reason to it stands in a Dip program. Anyway, they're beautiful pieces. For more Bartok, I would suggest the 14 Bagatelles, the Out of Doors Suite or the Sonatina. His music near always deals with nationalistic inspirations.
Berkeley, Sir Lennox (1903-1989, England) - Concert Study (1955). One of the most melodious composers I've ever heard, some kind of Mozart or Chopin of the 20th century in this specific trend. His output of piano music is large as well as obscure, but plenty of surprises. His language in general is a very extended tonality, full of what I can just describe as "British flavor".
Copland, Aaron (1900-1990, USA) - Scherzo (1920). One of the genious of early 20th century north-american music, that have coined revolutions in musical language, particularly in harmony and rhythm, apart and distinct from the european developments. His masterpiece is his Sonata, although it's a bit hard for this exam. I just wonder why there is no Cowell music in the program...
Debussy, Claude (1862-1918, France) - La plus que lente (1910), Preludes (1910-13), Suite Pour le Piano (1901). Oh, well...what can I say about him? One of the pillars of 20th century music in general, and the composer of one of the most magnificent sets of all times, the Preludes. By the way, "La Cathedrale engloutie" is a very good idea for any one who is wondering about a major modern piece.
Faure, Gabriel (1845-1924, France) - Just a remark: despite the fact he have several pieces composed into the 20th century, the available pieces are all from the past one: 1881, 1883 & 1894.
Hindemith, Paul (1895-1963, Germany) - Ludus Tonalis (1942). It's very difficult to write about his music, 'cause anything you read about it is deceptive: you should hear to understand the tricks of Herr Paul. Sometimes seems tonal, and suddenly: no tonality at all. This particular piece is a masterwork of mid-century piano music, and it's unbelievable that is not very played and known. A possible parallel to Bach's WTC, despite the fact that finding parallels to the WTC is always dangerous. Another very interesting work by him is the Suite 1922.
Janacek, Leos (1854-1928, former Czechoslovakia) - In the Mists (1912). Another masterpiece. Maybe I am wrong, but seems to happen a sort of "revival" of this composition: after years that I seldom heard to talk about it, there was in the last year at least three important concerts with this piece. Very closely related to Nationalism, but a very distinct approach compared to Bartok's.
McCabe, John (1939, England)- Five Bagatelles (1964). The first alive composer to be mentioned, and a wonderful pianist. The set is from a time when he was very tied to orthodox serialism.
Messiaen, Olivier (1908-1992, France)- Vingt Regards sur l'Enfant Jesus (1944). The father of french avant-garde, teacher of Boulez among others. The complete set is large, and deals with what the composer was more concerned about: Catholicism. The piano use is very original, and very tricky, sometimes highly virtuosistic. Let me do another comparison: Liszt after the war. However, the most astonishing piano work he composed is, in my humble opinion, the Quatuor pour la fin du temps (a chamber work with clarinet, violin and cello), one of the most dramatic and sensitive works I've ever heard.
Poulenc, Francis (1899-1963, France) - Toccata. Sorry, but this piece I actually don't know. It is in this list because I love his piano music, particularly the Improvisations. He was one of "Groupe des Six" (with Milhaud, Auric, Honegger, Tailleferre and Durey), the famous group of french composers inspired by Satie.
Prokofiev, Sergey (1891-1953, Ukraine) - Visions Fugitives (1917). Masterpiece among masterpieces (just remember the Sonatas, for instance). One of the scores that I would bring to the desert island. What more can I say?
Ravel, Maurice (1875-1937, France) - Sonatine (1905). This is a piece to make any audience very happy. A light approach to the sonata, with all that harmonies associated to him and to Debussy, and melodic finds that makes you cry. Furthermore, it's a very good introduction to Ravel's piano music, full of masterpieces such as: Miroirs, Valses nobles et sentimentales, Le tombeau de Couperin, and - last but not least - Gaspard de la nuit.
Schoenberg, Arnold (1874-1951, Austria) - Sechs kleine klavierstucke opus 19 (1911). A set made by the father of serialism well before his achievment, in a time he was an Expressionist artist. Every and all of the pieces are very short, but deep and full of meaning and emotions. Of course, not the same kind of feelings that you find in Chopin, for instance, but they are pure poetry anyway. Similar but far from the same are the Klavierstucke opus 11, from 1909. But if you want to hear some Schoenberg's dodecaphonic music, try the Suite (the first complete work to use his technique) or the Klavierstuck opus 33a. And if you want to dig deep, listen to (or even better: attend to a live performance) Pierrot Lunaire, a chamber work with piano that is very very strange, but very very cool.
Skryabin, Alexander (1871/76-1915, Russia) - As Faure, the available pieces by him are not composed in the 20th century.
Shostakovich, Dmitri (1906-1975, Russia) - Preludes opus 34 (1933). OK! One of my favorites sets of all piano repertory, where the composer explores all sort of moods. In my series of analogies

, the opus 28 of the 20th century. His musical language is probably one of the most straight forward to nineteentish ears, although he's full of harmonic surprises. The rest of his piano music output requires attention, especially Aphorisms and the astonishing 24 Preludes and Fugues (any Bach's resemblance it's not mere coincidence).
Stravinsky, Igor (1882-1971, Russia) - Tango (1940). Last but not least, the great russian composer. He's one of the most important composers of all times, and with Schoenberg and Debussy the fundamental stones of modern music. However, since life is not perfect, I dislike a bit this piece and haven't heard it in a long while, so sorry for no further comments.