Hesitated to venture into this realm.
When was the Douay-Rheims published?
New Testament 1582, Old Testament 1609 – translations from the Latin Vulgate, which are translations from all the Hebrew, Aramaic, and Greek texts largely due to the efforts of St. Jerome (345-420) and declared to be the authentic Latin version of the Bible by the Council of Trent (1545-1563).
When was the King James published?
New and Old Testaments 1610 – translations of the New Testament from Greek, the Old Testament from Hebrew and Aramaic, the Apocrypha from Greek and Latin.
What are the Apocrypha? (Not the Apocalypse)
Many of these texts are considered canonical Old Testament books by the Catholic Church, affirmed by the Council of Rome (382) and later reaffirmed by the Council of Trent. Apocrypha are well attested in surviving manuscripts of the Bible. See Codex Vaticanus, Codex Sinaiticus, Codex Alexandrinus, Vulgate, and Peshitta.
Both the King James and the Douay-Rheims are eloquent from a literary point of view. The D-R is approved.