All eucharistic liturgies of the Catholic Church since the earliest days have included two distinct sections:
The Liturgy of the Word
The Liturgy of the Eucharist
While a lot of ‘windowdressing’ may be added in the form of introductory prayers, penitential texts, seasonal antiphons and the like, the basic structure is there.
Some things that are different-
The Eastern Church loves, I mean absolutely adores litanies… all over the place. In the Western Church these days we are lucky to get a litany at Mass once or twice a year…
Also, the Eastern Churches do not tend to employ hymnals with metric hymns such as we do in the west. Most hymns are proper to the day in the Eastern Churches, such as the Troparion. While the Latin, Ambrosian, and Mozarabic rites provide brief Introits/Entrance Antiphons and Communion Antiphons, the Troparion are lengthier, may paraphrase scripture but is often original material that is specifically reflective on the nature of the feast.
I do not know about the practice among Eastern Catholics, but with the Eastern Orthodox Churches I have attended, the Homily is preached after the Liturgy. Nothing interrupts the flow of the Divine Liturgy with the ordinary words of man.
You might observe in a very VERY few places some minor westernizations in the celebrations of Divine Liturgy in those Churches that are united with Rome. These are very strongly opposed by the Vatican which - especially since Vatican II - has called for the purity of the eastern rites to be restored. I have a wonderful book that predates V2 which gives pictoral and textual information on the celebration of the various Eastern Rites, but you can see an awful lot of westernizations - usually in vestments and vessels. Again, these are becoming more and more rare, but I am told they can still be found, especially in small, relatively poor parishes.
You may also want to keep in mind that you really have three - some would say four - streams of liturgical patrimony in the Church:
Latin - the Roman Rite (Tridentine and Pauline, as well as predecessors), the Ambrosian sub-rite and the Mozarabic sub-rite, as well as the order-specific versions of the Latin Rite for certain religious orders.
Byzantine - the Greco-Russian tradition draws from the Byzantine foundations of the churches from Greece through Russia itself, including the former iron-curtain countries (with an exception for Armenia, which is hard to classify… perhaps a fifth?)
Oriential - the Oriental tradition is most strongly exhibited in those Churches of the Maronite, Syrio-Malabarese and Syrio-Malankanarse (i.e., India) rites, as well as others. Some include the Coptic and Ethopian rites in the Oriental family, though others would argue against that. These rites descend from the Liturgies of St. James of Jerusalem and Addai and Mari and have a more semetic underpinning.
Hope all this rambling is of some assistance.
Rob+