The most compelling argument is not the historical events, however, as much as the similar themes and quotations between Obadiah and Jeremiah, giving credence to the thought that they were contemporaries. As for the terror of you, The arrogance of your heart has deceived you, O you who live in the clefts of the rock, Who occupy the height of the hill. The question comes if Jeremiah quotes Obadiah or if Obadiah quotes Jeremiah. One would put the date of Obadiah after the exile, giving credence to the third date. The other would give credence to the first two dates.
Differences are of the kid that come in transmission rather than original composition.
T.H. Robinsons's judgment that the material is more original in Obadiah, but better preserved in Jeremiah, can hardly be improved upon. This presumes that both drew on a common source that was older than either. The Sin of Edom Edom was arrogant and gloating in the woes of Judah. The message of God to the Edomites is simple. You should have helped your brother nation against his oppressors, for your destruction is next.