Is the liturgy of Saint James, the brother of God, the same in the Syriac Orthodox Church of Antioch as it is in the Greek Orthodox Church of Jerusalem?
The Syriac Liturgy of St James is a fifth-century translation of the original Greek. It rose to prominence amongst non-Chalcedonians throughout Mesopotamia, eventually replacing the native Mesopotamian anaphoras, but it was edited by Jacob Baradaeus (+578) and then underwent a substantial reformation in the 12th century renaissance of the Syriac Church. A major figure in the revision was Dionysius bar Salibi (+1171). The anaphora of St James itself is retained, but there are aspects of the rite that are unique to the Syriac, Arab, and other regional cultures of the middle ages. (As an aside: The anaphora of St. James is the model for all of the various anaphoras in the Syriac Church, of which there are more than sixty.)
Is the liturgy of Saint Basil in the Coptic Orthodox tradition the same as the liturgy of Saint Basil in the EO tradition?
The Coptic Liturgy of St Basil is actually based on a Syriac source (not a Cappadocian one). While the Coptic rites obviously constitute their own liturgical family (the Alexandrian), they were influenced by the Syriac Church in the middle of the sixth century and again during the Syriac renaissance in the middle ages. So was Ethiopia.
None of the above is surprising: All Orthodox (from Byzantines to Ethiopians) derive significant parts of their liturgical heritage from the Antiochene tradition. Either originally or in the fourth/fifth century or in the middle ages.