From an article by Jeffrey Tucker on music for Mass at the Vatican:
For Easter, he chooses Mass I (Lux et Origo), along with Mass IV (Cunctipotens Genior Deus) for the Feast of the Apostles. He also uses Credo I, III, and IV, and, periodically, the whole of Mass IX (Cum Jubilo). He is trying minimize the use of Mass of the Angels, though it is still programmed for large international Masses since this is the one that most people know.
These are all huge advances, and he is thrilled to hear that people are singing with gusto! Actually, people are singing as never before. He is careful to print large booklets for every Mass with translations. He is dedicated to making sure that he does not use modern notation in the booklets. He believes in neumes, the notation of the Church, because he regards them as easier to sing than modern notes and because they convey the sense that the music of the Church is different from other forms of music
The biggest advances have been made in the area of propers, which had long been displaced by hymns that are extraneous to the Mass. The Introit of the day is sung at every Mass as the celebrant approaches the altar, following a hymn or organ solo. The communion chant is always sung with Psalms from Richard Rice’s editions posted at MusicaSacra.com.
This is a major step and a restoration of a very early practice for Papal Masses. The offertory antiphon is also sung periodically and increasingly so as more and more singers can handle the material. For the Psalm, St. Peters is alternating the use the of the Gradual Psalm from the Graduale Romanum and the simpler Psalms from the Graduale Simplex.
Just now, the choirs are moving into the polyphonic repertoire of the Italian masters such as Palestrina and Victoria, and will be increasingly exploring polyphonic propers along with new compositions.