The dotted with eighths makes more sense if the tune is being sung in a broad (aka "stately") tempo, the half with quarters makes sense if it's being sung more flowingly to allow/encourage typical American Catholic congregants to sing each line (especially the first and third) in one unflagging breath without lifting.
The 1940 Hymnal appears to have introduced the two quarter notes. In versions earlier than that documented at Hymnary, the measure was a syllable on a half note followed by a syllable on a quarter note tied with two eighths.
I don't know that we can say that either one is 'correct'. I prefer the two eighths version, but in the absence of an 'urtext', that doesn't make it 'correct'.
[Teasing]: Since Anglicans (and former Anglicans) have been known to break spontaneously into SATB, surely the home country of such behavior is superior to its colonial derivative. Additionally, you've not heard congregational participation until you've heard mostly not-college-educated Welshmen sing Love Divine, All Loves Excelling, in unison, unaccompanied.
Even older hymnals have a half note for the first syllable, then a quarter (repeating the pitch of the half note) and two quarters (each going up a step) for the second syllable.
I.e. (if in the key of G major): g2 (g4 a8 b8), 1868. Also appears as: g2 (g8 a8 b4), 1900. And even as a half followed by a triplet (the oldest, melody in tenor, 1849. The dotted half version appears as early as 1906, in The English Hymnal with Tunes. The half followed by two quarters seems to have originated in The Hymnal 1940.
The New Oxford Book of Carols (ed. Keyte & Parrott) has very extensive notes about the tunes and texts in an appendix---My copy is at the church, but I have a meeting there this afternoon, so I will look up the notes for this tune and see what they say about it. IIRC, it was originally an aria Alla hornpipe from an English opera, and was adopted as a hymn tune for the hymnbook of the Methodist Lock Hospital in London, for the text "Lo, He comes an Infant Stranger".
Wikipedia shows a scanned page printed in 1758 with a great many rhythmic differences - dots, appoggiaturas, and triplets - that we don't see in any of our versions. Is that the 'correct' version? If you are looking for The English Hymnal version from 1906, the Vaughan Williams arrangement, that would be the eight notes.
I have never heard this in a Catholic church. Local Methodists (Isle of Man) are using something very like the 1758 version, with all its complexities, it often figures in ecumenical services and on festive occasions..
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