As someone who was a member of a Melkite parish for years, but then moved so am now a member of a Maronite parish, I can address some of the differences between the two.
Leaving aside the fact that the Melkites come from the Greek/Byzantine tradition and the Maronites from the Syriac tradition; and leaving aside the debate of the extent to which the Maronites are Latinized, here are some differences.
In terms of language, both Melkites and Maronites tend to use the vernacular of whatever country they’re in. In the “mother country” they both emphasize the use of Arabic, but once you get outside of the mother country other languages do abound. They still maintain a good deal of Arabic in their liturgies primarily because their parishes often consist largely of first, second and third generation immigrants, some of whom still speak Arabic almost exclusively.
This being said, their “traditional” liturgical languages are different. The Melkite’s official liturgical language is Greek, and the Maronite’s is Syriac.
Also liturgically, while the bird’s-eye view of their liturgies is similar, when one gets into details the two liturgies are quite different. In the “Liturgy of the Word,” for example, the central liturgical themes for the day in the Melkite/Byzantine tradition will be sung in the Troparia and Kontakia of the day. These are two rather short hymns that condense a good deal of theology into a couple of short phrases. They are easily remembered, and most Melkites/Byzantines can call them to mind at the drop of a dime. I haven’t been in a Melkite parish in two or three years now (
) and I can still remember the majority of the Troparia and Kontakia.
In the Maronite tradition, on the other hand, the major themes of the day are sung in the Hoosoyo, a much longer hymn that is not nearly as easy to memorize as the Troparia and Kontakia of the Byzantine tradition. The bulk of the Hoosoyo (called the Sedro) is typically sung by a deacon or subdeacon. It is preceded by an opening prayer - the Proemion - that functionally serves to condense the main themes of the Hoosoyo into a few lines. This prayer is sung by the priest. The Sedro is then followed by a hymn/qolo sung by the faithful to a metered melody. The entire Hoosoyo is then closed out with a closing prayer (Etro) again sung by the priest.
The cycle of readings between the Maronite and Melkite traditions are completely different.
The Byzantine tradition has maybe three Anaphoras (Chrysostom, Basil, and Presanctified), whereas the Maronite tradition currently has I think six or seven. Traditionally the Maronite tradition had even more, but these other Anaphoras have yet to be translated.
Theologically the Maronites tend to be more Christo-centric than the Melkites, who tend to emphasize more the role of the Trinity as a whole. This is not to say that the Maronites are not extremely Trinitarian in their theology and spirituality, but only that they are more Christo-centric than the Melkites (not as much as the Romans though). This is illustrated most explicitly in their singing of the Thrice-Holy/Qadeeshat Aloho. The Byzantines (and Romans for that matter) consider the Thrice-Holy Hymn to be a Trinitarian hymn, whereas the Maronites (and other Syriacs) consider it a Christological Hymn. For this reason the Maronites can add phrases like “who are risen to from the dead” after “holy immortal one” and not imply that it was the Trinity that suffered, died and was raised, but on the second Person of the Trinity.
In terms of spirituality, the Maronites are not really influenced by the hesychastic tradition of the Byzantines. Traditionally Maronite spirituality was focused on the liturgical life - particularly the celebration of the Divine Office culminating in the celebration of the Sunday Eucharist, study of Scripture (“study” here implying more a lectio divina-type study than an academic type study) and the writings of the saints, and the life of prayer which includes the interior battle against one’s passions. There is also a great emphasis on the role of the Virgin Mary in our spiritual lives. In modern popular piety the rosary maintains a central place. I’m given to understand, however, that this is also true in the other Syriac traditions as well. Because of the central role that devotion to Mary has played in the Maronite tradition, the rosary seems to be less of a Latinization and more of a convenient expression of an already deep-seated Marian tradition.
The Melkites, on the other hand, following the Byzantine tradition, emphasize more the hesychastic tradition and all that it implies.
Really the best way to learn the differences between the two traditions, is to just attend their liturgies, pay attention during them, ask questions afterwards, and really let the spirit of these two traditions speak to you! Both are amazing in their own way, but they ought to be taken on their own terms.