The Einheitsübersetzung is more or less avoided by Traditionalists. It is a very modernistic transliteration by an ecumenical group of theologians and linguists. The German is modern and flimsy, and very “inclusive.” However, it is the currently approved German translation for the OF Mass, so it is certainly useful in that sense.
The Herder-Bibel is a solid 20th Century translation. It was nicknamed the Benediktiner-Bibel long before HH Pope Benedict XVI. became Holy Father. The nickname is simply because the translation was primarily done by Benedictine monks.
However, neither of these is the German equivalent of the English Douay-Rheims. The Allioli-Bibel, translated by Joseph Franz von Allioli was the first German translation to receive a papal imprimatur in 1830. This was used liturgically as the official German translation of the Vulgata Clementina until the implementation of the Einheitsübersetzung after Vatican II.
The Herder-Bibel is an easier read, and is still beautiful German (similar to the Knox Revision in the UK or the Confraternity version in the US), but if you are looking for the exact German that would be used in a bilingual EF Missal or Breviary, the Allioli-Bibel is the one you want.