The Rite of Spring, is "primitivist" in that its programmatic subject is a pagan rite: a human sacrifice in pre-Christian Russia.
"The Rite of Spring" is harmonic in showing an aggressive tone. Under the broad sound, he shows dissonance, primitive rhythms, jarring orchestration, and folk melodies. Harmonically, he shows the pentatonic scale to create dissonances, and primitive chords. Melodically, Stravinsky shows traditional Russian folk music; he gives a horizontal shape to the piece, he allows the woodwinds to be the dominant part instead of the strings be what you hear most. Rhythmically, the music is very primitive and the beat of the piece is steady but is slightly disrupted with off-accents.
Symphony of Psalms is neotonal, it uses reiteration and other means to establish a tonal center, rather than traditional functional harmony. Neoclassicism allowed Stravinsky to use the tools he had developed in his Russian period while also showing a place in the classical tradition of the West.
There were more clearly perceived themes, and many were borrowed from both the classical period and newer trends at that time. The music avoided the exaggerated gestures and complex forms of the late romanticism. It was more emotionally restrained as well. It focused a lot on symmetry and was quite simple.
Primitivism is tonal, but the tonality is not achieved through expectation of resolution, as in the Common Practice Period, but through the asserting of one note as more important