In the Roman Rite, the Liturgy of the Hours is quite standard. In some places such as the European English speaking countries, the translations of the canticles and readings differ from those used in the U.S.
Most monasteries use a longer psalter (more psalms) and arrange psalms, etc. differently by permission of the Holy See.
With the Dominican Order to which I belong, (we are not monks, although we live a monastic styled life and chant the Hours) the psalm tones may differ from place to place, but the Hours themselves are the same around the world.
Fr. Vincent Serpa, O.P.