Hi Commenter.
There’s a couple of things you should know here. First, there is no “Eastern Catholic Church.” There are 23 or 24 Eastern Catholic Churches, each of which utilizes one of several liturgical/ritual traditions. So, for example, there are the Ukrainian Greek Catholic, the Melkite Greek Catholic, the Romanian Greek Catholic, and the Ruthenian Greek Catholic Churches. Each of these churches has its own clergy and hierarchy, and may have its own set of laws (they are churches sui iuris [i.e. self-governing]). Despite this, however, each of these churches utilize the Byzantine liturgical tradition, and were formed by/draw from the Byzantine spiritual and theological tradition.
Relevant to this thread, the Maronite Catholic Church is not Byzantine, but Syriac (even though we are somewhat unique within the Syriac tradition). We have our own liturgical tradition, our own hierarchy and clergy, our own spiritual and theological traditions, etc.
Each different liturgical tradition has its own Liturgy of the Hours. So, the Roman tradition has its own Liturgy of the Hours, the Byzantine tradition has its “Horologion” and other liturgical books for celebrating the Hours, the Maronite tradition has Shhimtho and other books needed for celebrating the Hours, the Coptic tradition has the Agpeya, etc.
The differences are actually very significant, even though the Psalms are typically the central feature of the LotH. The Byzantine tradition has a complex system of hymns and prayers woven around the Psalms. It is not formatted for private prayer, but for public prayer. And there is a book (called the “typica”) that governs which prayers and Psalms are sung, and which may be omitted. When the full service of “Morning Prayer” is celebrated in the Byzantine tradition, it can actually take several hours!
From what I’ve seen of translations of the Maronite Shhimtho directly from the Syriac text (and without abbreviations), the Psalm verses are typically alternated with brief hymns/prayers that expand or gloss on the verse and/or the feast of the day. However, in the current English translation in use throughout the U.S. (a translation from the French edition, which is a translation of the Arabic edition, which is a translation from the Syriac), the format was restructured and abbreviated to more closely reflect the Roman LotH and make it possible for use as a “private devotion.”