How to sing chant?

The Church is riven over this; not really but it should be if we actually took the General Instruction of the Roman Missal seriously and gave preference to Chant.

The problem is: how should chant be sung? This video shows two possibilities.
Solesmes gave us the regular form of the first example, where each note is given the same value, but with singers skill subtlely interpreting the text and music. This, the Solemnes Method developed in the mid nineteenth century. Accounts of singing chant before that, at least in France, suggest that it was sung very slowly but notes were give different  lengths according to their grouping's, thus a single  note was sung as a crochet but a tied or grouped set of notes would be treated as a set of half notes or quavers, this is what happens in the second example.

Interestingly, manuals on musical decoration of secular music from the sixteenth century would also point to trills or other decorations occurring in one beat, even if they contain three or more notes. Why should this not have also happened in chant, even at early period? Another issue raised by the Rhetorical Method concerns the freedom the musician has to add non-written decorations and embellishments. This seems to have been an issue with reformed monastic orders such as the Cistercians who despised not only unnecessary decoration in their buildings but also their music.

There are some informative  comments on the video here.