By "due cori" Handel (or whoever appended the title) meant not two vocal choirs but two choirs of instruments -- but even this is misleading, because he actually requires three instrumental groupings: one of strings and two each of pairs of oboes, bassoons, and horns. Handel pillaged only two earlier compositions in assembling the third concerto in this trio of works, composing almost all but the final movement fresh for a performance incorporated into a 1747 presentation of his oratorio Judas Maccabaeus.
So it's two wind choirs that are notable here, and Handel often writes for them antiphonally, one echoing the other. The first movement is a brief French overture, drawn in part from Handel's so-called "Fitzwilliam Overture" for two clarinets and horn, but substantially reworked. The second movement is a long Allegro, opening with antiphonal horn calls, then deploying the full ensemble as it chugs along at a variety of dynamic levels. The third movement, Allegro ma non troppo, consists of a 62-bar dialog between the two wind bands, a question-and-answer or sometimes merely echo routine involving phrases anywhere from one to four measures long. Handel wraps up the movement with a 24-bar tutti bringing in the strings.
The Adagio provides a minute and a half of D minor repose, the mood of which is broken by the Andante larghetto -- not the lugubrious music one might expect from the tempo marking, but a cheerful, if stately, exercise in antiphony contrasting all the colors of the orchestra, including the strings. The concluding Allegro, with its brilliant and difficult horn writing (especially at the beginning), is a rewrite of a hunting aria from Handel's 1730 opera Partenope; the music develops into a gigue, with the horn calls continuing throughout.