The NOBC was intended as a supplement to the OBC, rather than a replacement of it, as the editors are quick to point out; where there is overlap between the two, the NOBC tends to supply variants of the standard carols, or well-needed commentary, whereas the OBC included few variants of a carol--only primary versions--and supplied scanty notes.

I prefer the NOBC as having carols that are more off the beaten track. The initial carols, due to their antiquity, free rhythms and fugal arrangements, may be less suitable for garden-variety caroling, but the bulk of the book contains many delightful carols--when I come across a "new" carol (new to me), I'm surprised at how often I find it lurking in the NOBC. Having made a sweep through the OBC, it was soon clear to me that most carols unfamiliar to me had such dishwater-dull tunes, it was no surprise they weren't performed more often. The variants in the NOBC are generally superior in this respect.

This is not to demean the efforts of Dearmer et al., since they were only providing the carols as they came to them (arrangement aside). Much worse for dull tunes are some of the older collections, like the Stainer and Cowley collections. It's curious how so many supposedly inspired people have written such dreadfully uninspiring tunes!


Adam lay ybounden: Per the NOBC the text is from a 15th c. manuscript (the Sloan Manuscript, in the British Library, MS 2593), which also contained the text of "Lullay, my liking (myn lyking)". [Per the Wikipedia article on this song, the BL estimates the text origin at ca. 1400] No setting from that period, or, apparently, from the ages in between, has survived; the popular settings are all at least 20th c. That in the OBC was written by Peter Warlock (Philip Heseltine). [My notes don't include a date, but the publication of the OBC makes it no later than 1928. A couple of Warlock's carol settings are now in the public domain (at least, in the US), having been published before 1923.]

The Wikipedia article contains additional illumination:
http://en.wikipedia.org/wiki/Adam_lay_ybounden

There's already a thread on "Down in Yon Forest" with good information. As for age, it depends whether you're talking about the "Corpus Christi" carol or the version John Jacob Niles collected, (re)arranged and copyrighted in 1935. The former goes back to the Renaissance. For more information, I defer to other threads, primarily this one:
Lyr Req: Down in Yon Forest (from John Jacob Niles): http://www.mudcat.org/thread.cfm?threadid=10671