The Antiochians/Greeks don't use the Psalms for the antiphons, nor do they say the Beatitudes.
Their loss. :)
The Beatitudes (third Antiphon) are my favorite part of at the beginning of the Divine Liturgy -- they just about define what Christianity is all about.
But these differences do not change the Divine Liturgy, just as the homily given either after the reading of the Gospel or at the end of the Divine Liturgy doesn't.