Mozart's Requiem (K. 626) is a milestone of 18th Century choral music, and is one of the most celebrating pieces of all time. Adding to the intrigue surrounding the piece, is the fact that Mozart died before it was completed. His wife Constanze hired the composer Franz Xaver Süssmayr to complete the work, and make it performable. Given the enormity of this task, Süssmayr, a minor composer, exceeded expectations, and his score remains the most performed version of the piece today. There is debate within the scholarly community about authorship, with some insisting that the sections attributed to Süssmayr far exceed his compositional ability, while others point to the fact that his sections contain minor compositional errors (parallel fifths, and things of that sort) that are simply not found in Mozart's output. Whatever Süssmayr's real contributions were, he is a major figure in the Requiem's history, and his work is an essential element of the piece's performance history.
Fast forward to the late 20th Century. Some musicologists have decided to revisit the score and correct the (albeit minor) problems that are found in it. Now this is considered to be a controversial notion. Some would ask if it is really defensible to tinker with a work that has stood the test of time, and is rightly considered a masterpiece. Furthermore, is it possible for modern ears to have any say in how this work "should sound," or are we far too removed from its original context? There have been several approaches, each with its own unique features. A layer of intrigue was added when, in 1962, a fragment of music from an Amen fugue was discovered, leading historians to believe it originally belonged as part of the Requiem, but no one is completely sure.
The musicologist Richard Maunder put forward a completion which omitted anything not thought to be written by Mozart, therefore eliminating two entire movements from the piece, but adding the Amen fugue. This seems like an extreme approach, first, because it is impossible to know exactly what was sketched out by Mozart himself, and also because it results in the exclusion of some very good music.
Duncan Druce takes an equally radical approach, but instead rewrites rather than eliminates the Süssmayr sections. Like Maunder, he adds the Amen fugue. This product, in some places, sounds quite far-removed from the original score. The Lacrimosa movement in particular is difficult to recognize in its new form. This is surely problematic. The Lacrimosa movement, even if not entirely written by Mozart is an iconic section that is strongly identified with the composer (even being used in the burial scene in the movie Amadeus, for example). Turning this movement on its head is a questionable choice.
Robert D. Levin's answer lands somewhere in the middle, using the Amen fugue like the others, but still addressing the project conservatively with the great care it deserves. He writes:
"The completion heard here seeks to respect both of the tendencies of the newer versions. On the one hand the compositional problems of the Lacrimosa and the Amen fugue, and the movements surviving only in Süssmayr's hand have not been overlooked out of blind piety before their 200-year-old origin. On the other hand, the historical and performance tradition of the Requiem demands respect. A clearly drawn line of separation, in which everything except the contents of Mozart's autograph draft was to be considered spurious per se, was explicitly rejected. Quite the contrary: the goal was to revise not as much, but as little as possible, attempting in the revisions to observe the character, texture, voice leading, continuity and structure of Mozart's music. I have retained the traditional version insofar as it agrees with idiomatic Mozartean practice."
I personally find Levin's approach the most convincing from a philosophical standpoint, but more importantly, the music itself sounds convincing. You might say it takes a certain amount of hubris to attempt to improve on a masterpiece. This is certainly true, so then I would say a little hubris can be healthy for artistic advancement. If we never tried new things or reinterpreted old things, we would not be where we are today. Part of what makes Mozart's Requiem so great is its mystery. If we could solve all the unanswered questions, perhaps we would not enjoy the work as much as we do today. Debate and discussion is half the fun.