As composer of this piece Bach has been mentioned, but based on more recent research Vetter seems a more likely candidate as the composer.
The compositions consists of three different treatments of the choral melody. The first and last of these three are identical for the first 8 bars and feature both a contrapuntal treatment of the choral melody. The second one features the chorale in the upper part, with the pther two parts providing a fast moving accompaniment. To be honest, this variatio could have been composed by Buttstett as well.
The source for this publication is manuscript US-NH LM 4843 [Ma2.Y11.B12], owned by the University of Yale. It is a very difficult to read source, and the musical text is often unclear or erraneous. Voices disappear and reappear at random, and often chords are extended further than just the three or four voices of a particular variatio. In the first variatio of this composition the use of the pedal is indicated once, where it seems likely that at least the last entry of the choral subject is meant for pedals as well. And there is the strange fact that in the manuscript the third variatio is called a fugue, where it is not a fugue at all. The first of the three, however, actually is a fugue on the first phrase of the chorale melody, yet is simply called "Allebreve".
Score available here: http://partitura.org/index.php/johann-nicolaus-vetter-nun-freut-euch-lieben-christen-gmein-emans-137